The Turkey international pens a four-year deal at the Turk Telekom Arena to finally complete his protracted move to Istanbul and end his unhappy spell in the Spanish capital
The 29-year-old only joined Los Blancos last summer on a free transfer from Bayern Munich, but a mix of injuries and failure to earn a first-team spot saw him appear just five times in La Liga, scoring once.
Accordingly, he has decided to move on rather than wait for his chance under Jose Mourinho, and will now prepare for his maiden spell in Turkey, having never previously played in the country of his descent.
According to Gala's official website, Hamit, also formerly of Schalke, has agreed a four-year contract, earning €2.9m (£2.3m) for the first two years and €2.75m (£2.16m) for the latter.
Hamit's becomes Galatasaray's third signing of the summer, following the footsteps of Umut Bulut and Dany Nounkeu. Meanwhile, the club are working hard to bring in Trabzonspor's in-demand forward Burak Yilmaz.