POWER OF ATTORNEY

       The undersigned, as a Section 16 reporting person of Omeros Corporation
(the "Company"), hereby constitutes and appoints 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 10th day of June, 2019.

                                    Signature: /s/ Peter Cancelmo
                                               ---------------------
                                               Peter Cancelmo