It was the fourth major move by Seattle this week after acquiring goalkeeper Stefan Frei from Toronto, forward Tristan Bowen from Chivas USA and defender Chad Marshall from Columbus. 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.
Moffat, 27, had a brief stint in Seattle. He joined the Sounders via trade with Houston in September. He made six appearances and four regular season starts for Seattle and started all three playoff games.