Exhibit 5.1

Skadden, Arps, Slate, Meagher & Flom LLP

Four Times Square

New York, New York 10036

(212) 735-3000

June 26, 2015

American Capital Agency Corp.

2 Bethesda Metro Center, 14th Floor

Bethesda, Maryland 20814

Re:American Capital Agency Corp. Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special counsel to American Capital Agency Corp., a Delaware corporation (the “Company”), in connection with the automatic shelf registration statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”). The Registration Statement relates to the issuance and sale from time to time by the Company, pursuant to Rule 415 of the General Rules and Regulations promulgated under the Act, of the following securities of the Company: (i) an indeterminate number of shares of the Company’s common stock, par value $0.01 per share (the “Common Stock”), (ii) an indeterminate number of shares of the Company’s preferred stock, par value $0.01 per share (the “Preferred Stock”), (iii) an indeterminate number of shares of Common Stock as may be issued upon conversion of any Preferred Stock or Debt Securities (as defined below) (collectively, the “Indeterminate Securities”), (iv) an indeterminate number of shares of Preferred Stock represented by depositary shares (“Depositary Shares”) evidenced by depositary receipts (“Receipts”), which may be issued pursuant to one or more deposit agreements to be entered into between the Company and a depositary to be named therein (each, a “Deposit Agreement”), and (v) and an indeterminate aggregate amount of debt securities (the “Debt Securities”) to be issued in one or more series under an indenture between the Company and U.S. Bank National Association, as trustee (the “Trustee”), the form of which is filed as an exhibit to the Registration Statement (together with any supplement thereto establishing the terms of any series of the Debt Securities, the “Indenture”). The shares of Common Stock, shares of Preferred Stock, Indeterminate Securities, Depositary Shares and Debt Securities to be offered pursuant to the Registration Statement are collectively referred to herein as the “Offered Securities.

This opinion is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of:

(i)     the Registration Statement;

(ii)     the Amended and Restated Certificate of Incorporation of the Company, as amended to date, as certified by the Secretary of State of the State of Delaware and the Secretary’s Certificate (as defined below) (the “Certificate of Incorporation”);

(iii)     the Second Amended and Restated By-laws of the Company, as currently in effect, as certified by the Secretary’s Certificate (the “By-laws”);

(iv)     certain resolutions of the Board of Directors of the Company (the “Board”) relating to the Offered Securities, as certified by the Secretary’s Certificate;

(v)     an executed copy of the certificate of Samuel A. Flax, the Executive Vice President and Secretary of the Company, dated the date hereof (the “Secretary’s Certificate”);

(vi)     a specimen certificate representing the Common Stock; and

(vii)     the form of the Indenture, including the form of notes to be issued thereunder.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company, and such agreements and certificates of public officials, certificates of officers or other representatives of the Company and others and such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinions set forth herein.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified, conformed or photostatic copies, and the authenticity of the originals of such copies. In making our examination of executed documents or documents to be executed, we have assumed that the parties thereto, other than the Company, had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents, and the validity and binding effect thereof on such parties. We have also assumed that the Indenture and any supplemental indenture to the Indenture establishing the terms of any Debt Securities will be duly authorized, executed and delivered by the Trustee, and that any Debt Securities that may be issued pursuant to the Indenture will be manually signed or countersigned, as the case may be, by duly authorized officers of the Trustee. In addition, we have assumed that the terms of the Offered Securities will have been established so as not to, and that the execution and delivery by the Company of, and the performance of its obligations under, the Indenture, any supplemental indenture to be entered into or company order to be issued in connection with the issuance of any Debt Securities, and any Deposit Agreement to be entered into in connection with the issuance of Depositary Shares, will not, violate, conflict with or constitute a default

under (i) any agreement or instrument to which the Company or its properties are subject (other than those agreements and instruments that are listed in Part II to the Registration Statement), (ii) any law, rule or regulation to which the Company or its properties is subject (other than Opined on Law, as defined below), (iii) any judicial or regulatory order or decree of any governmental authority (other than those under Opined on Law) or (iv) any consent, approval, license, authorization or validation of, or filing, recording or registration with, any governmental authority (other than those under Opined on Law). As to any facts material to the opinions expressed herein which we have not independently established or verified, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others.

Our opinions set forth herein are limited to the General Corporation Law of the State of Delaware (the “DGCL”) and the laws of the State of New York that, in our experience, are normally applicable to transactions of the type contemplated by the Registration Statement and, to the extent that judicial or regulatory orders or decrees or consents, approvals, licenses, authorizations, validations, filings, recordings or registrations with governmental authorities are relevant, to those required under such laws (all of the foregoing being referred to as “Opined on Law”). We do not express any opinion with respect to the laws of any jurisdiction other than Opined on Law or as to the effect of any such non-Opined on Law on the opinions herein stated. The Offered Securities may be issued from time to time on a delayed or continuous basis, and this opinion is limited to the laws, including the rules and regulations, as in effect on the date hereof, which laws are subject to change with possible retroactive effect.

Based upon and subject to the foregoing and to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that:

1.     With respect to any shares of Common Stock to be offered by the Company, including any Indeterminate Securities, pursuant to the Registration Statement (the “Offered Common Shares”), when (i) the Registration Statement has become effective under the Act, (ii) an appropriate prospectus supplement or free writing prospectus with respect to the Offered Common Shares has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (iii) if the Offered Common Shares are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Common Shares, including with respect to any Indeterminate Securities issuable in respect of conversion rights of Preferred Stock or Debt Securities registered pursuant to the Registration Statement, has been duly authorized, executed and delivered by the Company and the other parties thereto, (iv) the Board, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance and sale of the Offered Common Shares, the consideration to be received therefor and related matters, (v) if the issuance of the Offered Common Shares is certificated, certificates approved by the Board and in the form required by the DGCL and the By-Laws representing the Offered Common Shares are duly executed and countersigned, and (vi) the Offered Common Shares are registered in the Company’s share registry and delivered (A) upon payment of the agreed upon consideration therefor in accordance with any applicable underwriting agreement with respect to the Offered Common Shares or any other duly authorized, executed and delivered

valid and binding purchase or agency agreement or (B) upon the proper conversion or exercise (including, without limitation, if applicable, the payment of the proper conversion or exercise consideration) of the Preferred Stock or Debt Securities providing for said conversion or exercise, in any such case, as contemplated by the Registration Statement, the prospectus included therein and any applicable prospectus supplement or free writing prospectus, the Offered Common Shares (including any Offered Common Shares duly issued upon conversion of any Preferred Stock or Debt Securities) will be duly authorized, validly issued, fully paid and non-assessable, provided that the consideration therefor is not less than the par value thereof and the Certificate of Incorporation as then in effect authorizes the issuance of such number of shares of Common Stock.

2.     With respect to the shares of any series of Preferred Stock to be offered by the Company pursuant to the Registration Statement (the “Offered Preferred Shares”), when (i) the Registration Statement has become effective under the Act, (ii) an appropriate prospectus supplement or free writing prospectus with respect to the Offered Preferred Shares has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (iii) if the Offered Preferred Shares are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Preferred Shares, including with respect to any Indeterminate Securities issuable in respect of conversion rights of such Offered Preferred Shares, has been duly authorized, executed and delivered by the Company and the other parties thereto, (iv) the Board, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance, sale and terms of the Offered Preferred Shares, the consideration to be received therefor and related matters, including the adoption of a Certificate of Designation for the Offered Preferred Shares (each, a “Certificate of Designation”) in accordance with Certificate of Incorporation, By-Laws and the applicable provisions of the DGCL, (v) such Certificate of Designation has been filed with the Secretary of State of the State of Delaware and become effective, (vi) if the issuance of the Offered Preferred Shares is certificated, certificates approved by the Board in the form required by the DGCL, the applicable Certificate of Designation and the By-Laws representing the Offered Preferred Shares are duly executed and countersigned, and (vii) the Offered Preferred Shares are registered in the Company’s share registry and delivered upon payment of the agreed upon consideration therefor in accordance with any applicable underwriting agreement with respect to the Offered Preferred Shares or any other duly authorized, executed and delivered valid and binding purchase or agency agreement, the Offered Preferred Shares, when issued and sold or otherwise distributed will be duly authorized, validly issued, fully paid and non-assessable, provided that the consideration therefor is not less than the par value thereof and the Certificate of Incorporation as then in effect authorizes the issuance of such number of shares of Preferred Stock.

3.     With respect to any Depositary Shares representing fractional interests in any series of the Preferred Stock to be offered by the Company (the “Offered Depositary Shares”), when (i) the Registration Statement (including all necessary post-effective amendments), has become effective under the Act, (ii) an appropriate prospectus supplement or free writing prospectus with respect to the Offered Depositary Shares has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (iii) if the Offered Depositary

Shares are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Depositary Shares has been duly authorized, executed and delivered by the Company and the other parties thereto, (iv) the Board, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance and terms of the Offered Depositary Shares and the related series of Preferred Stock, including the adoption of a Certificate of Designation for such related series of Preferred Stock in the form required by the DGCL, the consideration to be received therefor and related matters, and the execution and delivery of the Deposit Agreement, (v) such Certificate of Designation has been duly filed with the Secretary of State of the State of Delaware and become effective, (vi) the applicable Deposit Agreement has been duly executed and delivered, (vii) the related shares of Preferred Stock have been duly authorized and validly issued in accordance with the DGCL and delivered to the applicable depositary for deposit in accordance with the Deposit Agreement, and (viii) the Receipts evidencing the Depositary Shares have been duly issued against deposit of the related shares of Preferred Stock with the applicable depositary in accordance with the applicable Deposit Agreement, the issuance and sale of the Depositary Shares will be validly issued and the Receipts will entitle the holders thereof to the rights specified therein and in such Deposit Agreement.

4.     With respect to any series of Debt Securities offered by the Company (the “Offered Debt Securities”), when (i) the Registration Statement (including all necessary post-effective amendments), has become effective under the Act, (ii) an appropriate prospectus supplement or free writing prospectus with respect to any Offered Debt Securities has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (iii) if the Offered Debt Securities are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Debt Securities, including with respect to any Indeterminate Securities issuable in respect of conversion rights of such Offered Debt Securities, has been duly authorized, executed and delivered by the Company and the other parties thereto, (iv) the Board, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance, sale and terms of the Offered Debt Securities and related matters, (v) any supplemental indenture in respect of such Offered Debt Securities has been duly authorized, executed and delivered by each party thereto, or company order in respect of such Offered Debt Securities duly adopted by the Board or authorized committee thereof or officer appointed thereby, (vi) the terms of the Offered Debt Securities and of their issuance and sale have been duly established in conformity with the Indenture and any supplemental indenture or company order to be entered into or adopted in connection with the issuance of such Offered Debt Securities so as not to violate any applicable law, the Certificate of Incorporation or By-laws or result in a default under or breach of any agreement or instrument binding upon the Company, and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, and (vii) the Offered Debt Securities have been duly executed and authenticated in accordance with the provisions of the Indenture and any such supplemental indenture or company order to be entered into or adopted in connection with the issuance of such Offered Debt Securities and duly delivered to the purchasers thereof upon payment of the agreed-upon consideration therefor, the Offered Debt Securities, when issued and sold in accordance with the Indenture and any such supplemental indenture or company order to be

entered into or adopted in connection with the issuance of such Offered Debt Securities and the applicable underwriting agreement, if any, or any other duly authorized, executed and delivered valid and binding purchase or agency agreement, will be valid and binding obligations of the Company, enforceable against the Company in accordance with its terms, except to the extent that enforcement thereof may be limited by (a) bankruptcy, insolvency, reorganization, fraudulent conveyance, moratorium or other similar laws now or hereafter in effect relating to creditors’ rights generally, (b) general principles of equity (regardless of whether enforceability is considered in a proceeding at law or in equity), (c) public policy considerations which may limit the rights of parties to obtain remedies, and (d) governmental authority to limit, delay or prohibit the making of payments outside the United States or in foreign currencies, currency units or composite currencies.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also hereby consent to the use of our name under the heading “Legal Matters” in the prospectus which forms a part of the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

Very truly yours,

/s/ Skadden, Arps, Slate, Meagher & Flom LLP