Exhibit 99.3

LETTER TO BROKERS, DEALERS

COMMERCIAL BANKS, TRUST COMPANIES

AND OTHER NOMINEES

Offer by

MOUNTAIN MERGER SUB CORPORATION

a wholly owned subsidiary

of

ANNALY CAPITAL MANAGEMENT, INC.

to Exchange Each Outstanding Share of Common Stock of

MTGE INVESTMENT CORP.

for

$9.82 in Cash and

0.9519 Shares of Common Stock of Annaly Capital Management, Inc.

or

$19.65 in Cash

or

1.9037 Shares of Common Stock of Annaly Capital Management, Inc.

(subject in each case to the election procedures and, in the case of an election of all-cash consideration or all-stock consideration, to the proration procedures described in the prospectus/offer to exchange and the related letter of election and transmittal)

THE OFFER AND THE WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., EASTERN TIME, ON JUNE 18, 2018, UNLESS EXTENDED. SHARES TENDERED PURSUANT TO THE OFFER MAY BE WITHDRAWN AT ANY TIME PRIOR TO THE EXPIRATION OF THE OFFER.

May 16, 2018

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

We have been engaged by Mountain Merger Sub Corporation (the “Offeror”), a wholly owned subsidiary of Annaly Capital Management, Inc. (“Annaly”), which is offering, upon the terms and subject to the conditions set forth in the enclosed prospectus/offer to exchange dated May 16, 2018 (as it may be amended or supplemented from time to time, the “prospectus/offer to exchange”) and related letter of election and transmittal (together, the “offer”), to exchange for each issued and outstanding share of common stock of MTGE Investment Corp. (“MTGE Common Stock”), at the election of the holder:

• the mixed consideration ($9.82 in cash and 0.9519 shares of Annaly common stock);

• the all-cash consideration ($19.65 in cash); or

• the all-stock consideration (1.9037 shares of Annaly common stock),

without interest and less any applicable withholding taxes, and subject to the election procedures and, in the case of an election of all-cash election or all-stock consideration, to the proration procedures described in the prospectus/offer to exchange and the related letter of election and transmittal.

YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., EASTERN TIME, ON JUNE 18, 2018, UNLESS EXTENDED.

There is no procedure for guaranteed delivery in the offer and, therefore, tenders must be received by the Expiration Time.

For your information and for forwarding to your clients for whose accounts you hold shares of MTGE Common Stock registered in your name or in the name of your nominee, we are enclosing the following documents:

1. The prospectus/offer to exchange dated May 16, 2018;

2. The related letter of election and transmittal for your use in accepting the offer and tendering shares of MTGE Common Stock and for the information of your clients; and

3. A printed form of letter which may be sent to your clients for whose accounts you hold shares of MTGE Common Stock registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the offer.

Annaly will not pay any commissions or fees to any broker, dealer or other person, other than to us, as the information agent, ComputerShare, as the exchange agent, and other persons described in the section of the prospectus/offer to exchange titled “The Offer—Fees and Expenses,” for soliciting tenders of share of common stock of MTGE Investment Corp. pursuant to the offer. Upon request, Annaly will reimburse you for customary clerical and mailing expenses incurred by you in forwarding any of the enclosed materials to your clients.

Any inquiries you may have with respect to the offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the information agent at the addresses and telephone numbers set forth on the back cover of the prospectus/offer to exchange.

Very truly yours,

D.F. King & Co., Inc.

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU THE AGENT OF ANNALY, OFFEROR, D. F. KING & CO. INC. AS THE INFORMATION AGENT OR COMPUTERSHARE AS THE EXCHANGE AGENT OR ANY AFFILIATE OF ANY OF THEM OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE ENCLOSED DOCUMENTS AND THE STATEMENTS CONTAINED THEREIN.