Gundogan, 34, made 358 appearances across two spells with City, scoring 65 goals and winning 14 trophies, including the Premier League, FA Cup and Champions League treble in 2023 when he captained the side.
Gundogan initially joined City from Borussia Dortmund in 2016 before moving to Barcelona in 2023. He returned to Manchester for the 2024/25 campaign, scoring five goals and making eight assists from 54 games across all competitions.
Galatasaray announced on Tuesday that they had reached an agreement with City for the free transfer of Gundogan until the end of the 2026/27 season.
Gundogan will earn a net salary of 4.5 million euros ($5.27 million) in each of the 2025/2026 and 2026/2027 seasons, Galatasaray said.
"I have no doubts Manchester City will enjoy much more success in the future and I will certainly be watching on from afar as I continue my career in Turkey, a country that means ever such a lot to me," Gundogan, whose parents are Turkish, said.
"Manchester City will always hold a special place in my heart. To win the Premier League and FA Cup trophies meant so much to me but to then be afforded the opportunity of lifting the Champions League trophy for this Club for the first time, especially in Istanbul, will live with me forever."