EXCEPTED HOLDER CERTIFICATE AND WAIVER

Exhibit 10.4

EXCEPTED HOLDER CERTIFICATE AND WAIVER

The undersigned duly authorized representative of U.S. Government Properties Income & Growth Fund, LP, a Delaware partnership (the “Fund”), has executed this Excepted Holder Certificate and provided it to Easterly Government Properties, Inc., a Maryland corporation (the “Corporation”), for the purposes described below. The Fund acknowledges and agrees that this Excepted Holder Certificate is a material inducement to the Corporation’s grant of the Waiver referred to below, and that the Corporation is relying on the accuracy of the representations and warranties, and compliance with the undertakings and agreements, contained in this Excepted Holder Certificate in granting the Waiver. The undersigned represents that it has authority to make the representations, warranties, undertakings and agreements contained herein on behalf of the Fund and acknowledges that the Waiver shall be void ab initio in the event that the undersigned lacks any such authority. Capitalized terms used herein but not otherwise defined have the meanings assigned to them in the Articles of Amendment and Restatement of the Corporation (the “Charter”).

R E C I T A L S

A. To help the Corporation maintain its status as a real estate investment trust (“REIT”) for federal income tax purposes under the Internal Revenue Code of 1986, as amended (the “Code”), the Charter imposes certain limitations on the ownership of the Corporation’s shares of Capital Stock, as set forth in Article VI of the Charter.

B. Section 6.2.7(a) of the Charter provides that, subject to Section 6.2.1(a)(iii) of the Charter, certain Ownership Limits, as defined in the Charter, may be waived (prospectively and/or retroactively) by the Corporation’s Board of Directors in its sole discretion, provided that certain conditions set forth in the Charter are satisfied, including receipt of certain representations and undertakings as may be required by the Corporation’s Board of Directors from the person seeking a waiver.

C. Pursuant to that Contribution Agreement by and among the Corporation, Easterly Government Properties LP (the “Operating Partnership”) and the Fund dated January 26, 2015 (“Contribution Agreement”), the Fund is contributing to the Operating Partnership all of its interests in certain entities and receiving common units of limited partnership interests of the Operating Partnership (“OP Units”) as of the closing date within the meaning of the Contribution Agreement (“Closing Date”). Subject to any applicable lock-up agreement, the Fund may exercise a put right on such OP Units, which the Operating Partnership may satisfy with Common Stock of the Corporation.

D. The Fund also expects to purchase shares of the Corporation’s Common Stock in connection with the Corporation’s initial public offering.

In connection with the Corporation’s waiver (the “Waiver”) of the Ownership Limits and the restriction in Section 6.2.1(a)(iv) of the Charter so as to permit the Fund to Beneficially Own and Constructively Own the Corporation’s Common Stock in an amount not exceeding 22.3% of the outstanding Common Stock of the Corporation (as more fully described below), subject to

the limitations described herein (the “Excepted Holder Limit”), and provided that each share of Capital Stock directly owned by the Fund and indirectly owned by a Beneficial Owner through its ownership in the Fund shall only be counted once in determining the aggregate Capital Stock held by the Fund and such Beneficial Owner, the undersigned hereby makes the following representations, warranties, undertakings and agreements on behalf of the Fund:

1. No “individual”, within the meaning of Section 542(a)(2) of the Code, as modified by Section 856(h)(3) thereof to exclude certain pension trusts from such definition, has Beneficially Owned or Constructively Owned, or will Beneficially Own or Constructively Own, through the Fund and any other owner of Common Stock (taking into account for this purpose that the Fund, since the Closing Date, has not Beneficially Owned or Constructively Owned, and will not Beneficially Own or Constructively Own, Capital Stock greater than the Excepted Holder Limit), Common Stock in excess of the Common Stock Ownership Limit and Capital Stock in excess of the Aggregate Stock Ownership Limit.

2. To its knowledge, the Fund does not Constructively Own a 9.9% or greater interest in any tenant of the Corporation or any subsidiary of the Corporation that is neither an individual nor the government of the United States or any agency or instrumentality thereof, as listed on Exhibit A. To its knowledge, the Fund does not Constructively Own a 9.9% or greater interest in any “independent contractor” (within the meaning of Section 856(d)(3)) of the Corporation, as listed on Exhibit B. In the event the Corporation proposes to sign a tenant that (i) is neither an individual nor the government of the United States or any agency or instrumentality thereof and (ii) is not listed on Exhibit A, or to contract with an independent contractor that is not listed on Exhibit B, the Corporation shall provide the names of such tenants or independent contractors to the Fund prior to entering into contracts with the same. The Fund shall inform the Corporation whether it can or cannot make this representation 2 with respect to such tenant or independent contractor. In the event the Fund is able to make the representation with respect to such tenant or independent contractor, such independent contractor or tenant shall be added to the list on Exhibit A or Exhibit B, as applicable, and this representation 2 shall apply with respect to such tenant or independent contractor and all other tenants or independent contractors listed on Exhibit A and Exhibit B. In the event the Fund informs the Corporation it cannot make this representation 2 with respect to such tenant or independent contractor, the tenant or independent contractor shall not be added to Exhibit A or Exhibit B, as applicable, and this representation shall only apply to the tenants and independent contractors listed on Exhibit A and Exhibit B.

3. The Fund acknowledges and agrees that the Capital Stock Beneficially Owned and Constructively Owned by the Fund remains subject to the restrictions and limitations set forth in Sections 6.2.1(a)(ii), 6.2.1(a)(iii), 6.2.1(a)(v) and 6.2.1(a)(vi) of the Charter.

4. The Fund acknowledges and agrees that the Waiver shall automatically be deemed to have been revoked (prospectively or, as necessary in order to protect the Corporation’s qualification as a REIT under the Code, retroactively) without any further action if any representation or warranty contained herein is or becomes incorrect or false, or any undertaking or agreement contained herein is breached, at the time of execution and delivery of this Excepted Holder Certificate or at any time thereafter.

2

5. The Fund acknowledges and agrees that the Waiver is only being granted to the Fund for the benefit of itself and the Beneficial Owners that Beneficially Own and Constructively Own Capital Stock as a result of the Fund’s Beneficial Ownership of any Common Stock purchased in connection with the Corporation’s initial public offering or received in connection with the exercise of the put rights in respect of the OP Units received pursuant to the Contribution Agreement, and is not being granted to any other Person.

Waiver: In reliance on the foregoing representations, warranties, undertakings and agreements, and subject to the limits and other provisions contained herein, the Fund is deemed to be an Excepted Holder under Section 6.2.7(a) of the Charter and the Corporation hereby grants this Waiver of Sections 6.2.1(a)(i)(1) and (2) and 6.2.1(a)(iv) for the sole and limited purpose of permitting (i) the Fund to Beneficially Own up to 22.3% in value of the Common Stock outstanding and (ii) any Constructive Ownership attributable to such Beneficial Ownership. This Waiver is limited to the Fund and any Constructive Owners of the Common Stock Beneficially Owned by the Fund that is permitted pursuant to this Waiver, and does not extend to any other Person.

[Remainder of Page Intentionally Left Blank]

3

This Excepted Holder Certificate is made as of the 11^th day of February, 2015 by the duly authorized representative of the undersigned.

[Excepted Holder Certificate and Waiver]