Exhibit 5.1

March 12, 2013

Apollo Residential Mortgage, Inc.

c/o Apollo Global Management, LLC

9 West 57th Street, 43rd Floor

New York, NY 10019

Ladies and Gentlemen:

We have acted as counsel to Apollo Residential Mortgage, Inc., a Maryland corporation (the “Company”), in connection with a registration statement on Form S-3 (File No. 333-182804), as amended (the “Registration Statement”), filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”). We are furnishing this letter to you in connection with the offer and sale by the Company of up to 7,820,000 shares (which includes 1,020,000 shares to be purchased pursuant to the underwriters’ option to purchase additional shares) of the Company’s common stock, par value $0.01 per share (the “Securities”), for issuance pursuant to the Underwriting Agreement, dated March 7, 2013 (the “Underwriting Agreement”), among the Company, ARM Manager, LLC and Morgan Stanley & Co. LLC.

In rendering the opinion expressed below, we have examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of the Registration Statement, the Prospectus and certain resolutions of the board of directors of the Company (the “Board of Directors”) and of a pricing committee of the Board of Directors (the “Pricing Committee”), relating to the transactions contemplated by the Underwriting Agreement and other related matters. As to factual matters relevant to the opinion set forth below, we have relied upon certificates of officers of the Company and public officials and representations and warranties of the parties set forth in the Underwriting Agreement.

Based on, and subject to, the foregoing, the qualifications and assumptions set forth herein and such other examination of law as we have deemed necessary, we are of the opinion that following the (i) issuance of the Securities pursuant to the terms of the Underwriting Agreement and (ii) receipt by the Company of the consideration for the Securities specified in the resolutions of the Board of Directors and of the Pricing Committee, the Securities will be legally issued, fully paid, and nonassessable.

CLIFFORD CHANCE US LLP

The opinion set forth in this letter relates only to the Maryland General Corporation Law. We express no opinion as to the laws of another jurisdiction and we assume no responsibility for the applicability, or effect of the law of any other jurisdiction.

We consent to the filing of this opinion as Exhibit 5.1 to a Current Report on Form 8-K that shall be incorporated by reference into the Registration Statement and to the reference to us under the caption “Legal Matters” in the prospectus supplement which is a part of the Registration Statement. In giving this consent, we do not concede that we are within the category of persons whose consent is required under the Securities Act or the rules and regulations of the Commission promulgated thereunder.

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