The Super Lig outfit announced the departure of the veteran coach on Tuesday, following lengthy meetings between the club's board members.
The 60-year-old - who recently took up a dual role in charge of the Turkey national team - had been in discussions over a new two-year deal. However, after talks broke down he has now been relieved of his duties.
Terim has overseen a disappointing start to the season, which leaves Gala sitting in 11th place in the Super Lig.
Under Terim's charge, they have taken just six points from their opening four games, with their derby clash against Besiktas abandoned on Sunday after supporters invaded the pitch at the Olympic Stadium.
Gala also have work to do in the UEFA Champions League after losing their Group B opener 6-1 at home to Real Madrid.
A statement on the club's official website read: "The Galatasaray Sports Club has decided to terminate the contract of coach Fatih Terim football. The club wishes him well in his future career."
During his third spell, Terim had resurrected a team that had finished eighth in the 2010-2011 Super Lig, taking them to back-to-back titles.
