The 31-year-old spent last season on loan with Ligue 1 outfit Marseille, scoring 20 goals in 31 league games before returning to the Liberty Stadium.
However, the France international was deemed surplus to requirements by Swansea boss Paul Clement and has now completed his move to Turkish side Galatasaray in a deal worth around £2.5m.
Hoş Geldin Bafetimbi Gomis! pic.twitter.com/KY7xcxTuJr— Galatasaray SK (@GalatasaraySK) June 29, 2017
Gomis scored 17 goals in 71 appearances during his two-year spell at the Liberty Stadium.