Exhibit 5.1

750 E. PRATT STREET  SUITE 900  BALTIMORE, MD 21202 T 410.244.7400  F 410.244.7742  www.Venable.com

August 14, 2017

Digital Realty Trust, Inc.

Four Embarcadero Center, Suite 3200

San Francisco, California 94111

Re: Registration Statement on Form S-4

Ladies and Gentlemen:

We have served as Maryland counsel to Digital Realty Trust, Inc., a Maryland corporation (the “Company”), in connection with certain matters of Maryland law arising out of the registration of up to 49,562,277 shares (the “Common Shares”) of common stock, $0.01 par value per share (the “Common Stock”), and 8,050,000 shares (the “Preferred Shares” and, together with the Common Shares, the “Shares”) of 6.625% Series C Cumulative Redeemable Perpetual Preferred Stock, $0.01 par value per share (the “Series C Preferred Stock”), of the Company, to be issued by the Company in connection with (a) the merger (the “REIT Merger”) of DuPont Fabros Technology, Inc., a Maryland corporation (“DFT”), with and into Penguins REIT Sub, LLC, a Maryland limited liability company (the “REIT Merger Sub”), and (b) the merger (the “OP Merger” and, together with the REIT Merger, the “Mergers” ) of Penguins OP Sub, LLC, a Maryland limited liability company (the “OP Merger Sub”), with and into DuPont Fabros Technology, L.P., a Maryland limited partnership (“DFT OP”), each pursuant to the Agreement and Plan of Merger, dated as of June 8, 2017 (the “Merger Agreement”), by and among the Company, REIT Merger Sub, Digital Realty Trust, L.P., Penguins OP Sub 2, LLC, a Maryland limited liability company, OP Merger Sub, DFT and DFT OP. The Shares are covered by the above-referenced Registration Statement, and all amendments thereto (the “Registration Statement”), filed by the Company with the United States Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “1933 Act”).

In connection with our representation of the Company, and as a basis for the opinion hereinafter set forth, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (herein collectively referred to as the “Documents”):

1. The Registration Statement, and the related form of joint proxy statement/prospectus, in the form in which it was transmitted to the Commission under the 1933 Act;

2. The charter of the Company (the “Charter”), certified by the State Department of Assessments and Taxation of Maryland (the “SDAT”);

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3. The Sixth Amended and Restated Bylaws of the Company, certified as of the date hereof by an officer of the Company;

4. The form of Articles Supplementary classifying and designating the terms of the Series C Preferred Stock, substantially in the form to be filed by the Company with the SDAT (the “Articles Supplementary”), certified as of the date hereof by an officer of the Company;

5. A certificate of the SDAT as to the good standing of the Company, dated as of a recent date;

6. Resolutions adopted by the Board of Directors of the Company relating to, among other matters, (i) the approval of the Mergers and the Merger Agreement, (ii) the filing of the Articles Supplementary with the SDAT and (iii) the issuance of the Shares (the “Resolutions”), certified as of the date hereof by an officer of the Company;

7. The Merger Agreement;

8. A certificate executed by an officer of the Company, dated as of the date hereof; and

9. Such other documents and matters as we have deemed necessary or appropriate to express the opinion set forth below, subject to the assumptions, limitations and qualifications stated herein.

In expressing the opinion set forth below, we have assumed the following:

1. Each individual executing any of the Documents, whether on behalf of such individual or another person, is legally competent to do so.

2. Each individual executing any of the Documents on behalf of a party (other than the Company) is duly authorized to do so.

3. Each of the parties (other than the Company) executing any of the Documents has duly and validly executed and delivered each of the Documents to which such party is a signatory, and such party’s obligations set forth therein are legal, valid and binding and are enforceable in accordance with all stated terms.

4. All Documents submitted to us as originals are authentic. The form and content of all Documents submitted to us as unexecuted drafts do not differ in any respect relevant to this opinion from the form and content of such Documents as executed and delivered. All Documents submitted to us as certified or photostatic copies conform to the original

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documents. All signatures on all Documents are genuine. All public records reviewed or relied upon by us or on our behalf are true and complete. All representations, warranties, statements and information contained in the Documents are true and complete. There has been no oral or written modification of or amendment to any of the Documents, and there has been no waiver of any provision of any of the Documents, by action or omission of the parties or otherwise.

5. Prior to the issuance of any Preferred Shares, the Articles Supplementary will be filed with, and accepted for record by, the SDAT.

6. Upon the issuance of any Common Shares, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under the Charter. We note that as of the date hereof there are more than 49,562,277 shares of Common Stock available for issuance under the Charter.

7. Upon the issuance of any Preferred Shares, the total number of shares of Series C Preferred Stock issued and outstanding will not exceed the total number of shares of Series C Preferred Stock that the Company is then authorized to issue under the Charter.

8. The Shares will not be issued or transferred in violation of any restriction on transfer and ownership of shares of stock of the Company set forth in the Charter or the Articles Supplementary.

Based upon the foregoing, and subject to the assumptions, limitations and qualifications stated herein, it is our opinion that:

1. The Company is a corporation duly incorporated and existing under and by virtue of the laws of the State of Maryland and is in good standing with the SDAT.

2. The issuance of the Shares has been duly authorized and, when and if issued and delivered in accordance with the Registration Statement, the Resolutions and the Merger Agreement, the Shares will be validly issued, fully paid and nonassessable.

The foregoing opinion is limited to the laws of the State of Maryland and we do not express any opinion herein concerning any other law. We express no opinion as to the applicability or effect of federal or state securities laws, including the securities laws of the State of Maryland, or as to federal or state laws regarding fraudulent transfers. To the extent that any matter as to which our opinion is expressed herein would be governed by the laws of any jurisdiction other than the State of Maryland, we do not express any opinion on such matter. The opinion expressed herein is subject to the effect of judicial decisions which may permit the introduction of parol evidence to modify the terms or the interpretation of agreements.

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The opinion expressed herein is limited to the matters specifically set forth herein and no other opinion shall be inferred beyond the matters expressly stated. We assume no obligation to supplement this opinion if any applicable law changes after the date hereof or if we become aware of any fact that might change the opinion expressed herein after the date hereof.

This opinion is being furnished to you for submission to the Commission as an exhibit to the Registration Statement. We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the use of the name of our firm therein. In giving this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the 1933 Act.

Very truly yours,

/s/ Venable LLP