The Sounders announced the signing on Thursday. Terms of the deal were not released by the club.
Seattle acquired Cooper last week in a trade with FC Dallas in exchange for midfielder Adam Moffat. Seattle also received allocation money from Dallas.
Cooper, 29, has made 188 career appearances since joining MLS in 2006 and has 72 goals and 16 assists. Last season for Dallas, Cooper had six goals and started 19 of 31 games played. Seattle is hoping Cooper can return to his form of two seasons ago with New York when he scored 18 goals in 33 games for the Red Bulls.