Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the following Registration Statements of our report dated February 19, 2015, relating to the consolidated financial statements of Apollo Residential Mortgage, Inc., and subsidiaries and the effectiveness of Apollo Residential Mortgage, Inc. and subsidiaries' internal control over financial reporting appearing in this Annual Report on Form 10-K of Apollo Residential Mortgage, Inc. for the year ended December 31, 2014.

1. Registration Statement No. 333-182804 on Form S-3 pertaining to a Universal Shelf for the offering of Common Stock, Preferred Stock, Depositary Shares, Warrants, and Rights.

2. Registration Statement No. 333-184921 on Form S-3 pertaining to Apollo Residential Mortgage, Inc.’s Direct Stock Purchase and Dividend Reinvestment Plan.

3. Registration Statement No. 333-175824 on Form S-8 pertaining to Apollo Residential Mortgage, Inc.’s 2011 Equity Incentive Plan.

/s/ DELOITTE & TOUCHE LLP

New York, New York

February 19, 2015