Exhibit 5.1

June 6, 2016

Easterly Government Properties, Inc.

2101 L Street NW, Suite 650

Washington, DC 20037

Ladies and Gentlemen:

This opinion letter is furnished to you in our capacity as counsel for Easterly Government Properties, Inc. (the “Company”) in connection with the Registration Statement on Form S-3 (File No. 333-210049) (as amended or supplemented, the “Registration Statement”) filed by the Company with the United States Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), and the prospectus supplement, dated June 1, 2016, filed by the Company with the Commission pursuant to Rule 424(b) under the Securities Act relating to the offering and/or sale of up to 6,126,967 shares of the Company’s common stock, par value $0.01 per share (“Common Stock”), which includes (i) the sale of 3,800,000 newly issued shares of Common Stock by the Company (the “Primary Shares”) to the underwriters (the “Underwriters”) named in an Underwriting Agreement (the “Underwriting Agreement”) among the Company, certain forward sellers (the “Forward Sellers”) and certain selling stockholders (the “Selling Stockholders”), (ii) the sale to the Underwriters by the Forward Sellers of 1,500,000 shares of Common Stock (together with the Primary Shares, the “Company Shares”), (iii) the sale to the Underwriters by the Selling Stockholders of 826,967 shares of Common Stock and (iv) the issuance and sale to certain forward counterparties (the “Forward Counterparties”) pursuant to letter agreements between the Company and the Forward Counterparties (the “Forward Sales Agreements”) (subject to the Company’s right to elect cash settlement or net share settlement in accordance with the terms of the Forward Sale Agreements) of 1,500,000 shares of Common Stock in the aggregate, subject to adjustment (the “Forward Shares”). The Company Shares also include up to 919,045 shares of Common Stock purchasable by the Underwriters upon their exercise of an option granted to the Underwriters by the Company. The Company Shares and the Forward Shares are collectively referred to herein as the “Shares.”

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the Maryland General Corporation Law (which includes reported judicial decisions interpreting the Maryland General Corporation Law).

Easterly Government Properties, Inc.

June 6, 2016

Page 2

For purposes of the opinion set forth below, we have assumed that a sufficient number of authorized but unissued shares of Common Stock will be available for issuance when the Forward Shares are issued.

Based on the foregoing, we are of the opinion that (i) the Company Shares have been duly authorized and, upon issuance and delivery against payment therefor in accordance with the terms of the Underwriting Agreement, the Company Shares will be validly issued, fully paid and nonassessable and (ii) the Forward Shares have been duly authorized and, upon issuance and delivery against payment therefor in accordance with the terms of the Forward Sales Agreement, the Forward Shares will be validly issued, fully paid and nonassessable.

This opinion is being furnished to you for submission to the Commission as an exhibit to the Company’s Current Report on Form 8-K relating to the Shares (the “Current Report”), which is incorporated by reference in the Registration Statement. We hereby consent to the filing of this opinion as an exhibit to the Current Report and the said incorporation by reference and to the use of the name of our firm therein. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ GOODWIN PROCTER LLP

GOODWIN PROCTER LLP