POWER OF ATTORNEY

       The undersigned, as a Section 16 reporting person of Omeros Corporation
(the "Company"), hereby constitutes and appoints Peter B. Cancelmo, Gregory A.
Demopulos, M.D., Michael A. Jacobsen, David R. Toll and Covington & Burling LLP,
as outside counsel to the Company, and each of them individually, as his or her
true lawful attorney in-fact and agent with full power of substitution, for him
or her in any and all capacities, to:

       1.   prepare, complete and execute in the undersigned's name and on his
            or her behalf, Forms ID, 3, 4 and 5, including all amendments
            thereto, as well as any other documents as the attorney- in-fact
            shall determine to be necessary or appropriate to obtain codes and
            passwords and make electronic filings with the United States
            Securities and Exchange Commission (the "Commission") under Section
            16(a) of the Securities Exchange Act of 1934, as amended (the
            "Exchange Act"), and the rules and regulations promulgated
            thereunder, or any successor laws and regulations, as a consequence
            of the undersigned's ownership, acquisition or disposition of
            securities of the Company;

       2.   perform any and all acts for and on behalf of the undersigned that
            may be necessary or appropriate in order to file such forms with the
            Commission, any stock exchange or similar authority and such other
            person or agency as the attorney-in-fact shall deem appropriate; and

       3.   take any other action of any type whatsoever in connection with the
            foregoing which, in the opinion of the attorney-in-fact, may be of
            benefit to, in the best interest of, or legally required by, the
            undersigned, it being understood that the documents executed by the
            attorney-in-fact on behalf of the undersigned pursuant to this Power
            of Attorney shall be in such form and contain such terms and
            conditions as the attorney-in-fact may approve in such attorney-in-
            fact's discretion.

       The undersigned hereby grants to each of the foregoing attorneys-in-fact
full power and authority to do and perform any and every act and thing
whatsoever requisite, necessary or proper to be done in the exercise of any of
the rights and powers herein granted, as fully to all intents and purposes as
the undersigned might or could do if personally present, with full power of
substitution or revocation, and hereby ratifies and confirms all that said
attorneys-in-fact, or the substitute or substitutes of said attorneys-in-fact,
shall lawfully do or cause to be done by virtue of this Power of Attorney and
the rights and powers herein granted. The undersigned acknowledges that the
foregoing attorneys-in-fact, in serving in such capacity at the request of the
undersigned, are not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16(a) of the Exchange Act.

       This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
Company and the foregoing attorneys-in-fact.

       IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 6 day of June, 2019.


                                          Signature:    /s/ Arnold Hanish
                                                        -----------------
                                                        Arnold Hanish