The Ivorian right-back joined the Reds from Villarreal in September 2022, where he featured regularly.
He made 24 Premier League appearances last term to help Forest achieve safety.
Injuries have limited him to just 13 matches this term, with the defender's last match for Forest coming on December 2.
And he has now swapped England for Turkey to link up with Super Lig giants Galatasaray in the club's quest to defend their league championship.
A Forest club statement read: "Serge Aurier has completed a permanent transfer to Turkish Super Lig side Galatasaray.
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"The 31-year-old joined Forest in September 2022 and went on to make 41 appearances for the Reds in all competitions.
"The defender, who has featured 13 times this season, now heads to Turkey to join Okan Nuruk's side.
"We would like to thank Serge for his contribution during his time at the City Ground and wish him well for the future."
He now links up with his ex-Tottenham teammates Davinson Sanchez and Tanguy Ndombele at the Ali Sami Yen Stadium.
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Despite his injury troubles of late, he was called up to represent Ivory Coast at the Africa Cup of Nations.
And he has so far featured three times in the tournament, with the Elephants preparing for their quarter-final clash against Mali on Saturday.
Aurier, who is Ivory Coast's captain, has featured 91 times for his nation.