The 31-year-old defender, currently on international duty in the Africa Cup of Nations, joined Forest in September 2022 and made 41 appearances in all competitions. He has featured 13 times this season.
The forest is 16th in the league standings, two points above the relegation zone.
Champions Galatasaray said Aurier had signed to the end of the season and a transfer fee of $107,850.00 would be paid to Forest.
"The player will be paid a net guarantee fee of $648 390 and a net signing fee of 150 000 euros for the 2023/2024 season," the Istanbul club added.
Aurier joins former Tottenham Hotspur teammates Davinson Sanchez and Tanguy Ndombele at Galatasaray.
--Reuters--