Bailly had been on the books of the Red Devils for seven years but spent last season on loan at French side Olympique Marseille, where he made 23 appearances.
The 29-year-old was Jose Mourinho's first signing as Manchester United manager in the summer of 2016, joining from Villarreal for £30m.
Bailly would go on to make 113 appearances for the Red Devils, winning the Europa League and Carabao Cup in his time at Old Trafford.
Despite the transfer window closing in most of the major leagues in Europe, that of Turkey runs until September 15.
A statement from the Turkish Super Lig side said: "Our club has reached an agreement with Manchester United for the final transfer of Ivorian defender Eric Bailly.
"We wish Eric Bailly, who we believe will provide important services to our club, great success with our glorious jersey, and present it to the public with our respect."
Bailly has won 49 caps for Ivory Coast and was a key member of their 2015 Africa Cup of Nations winning squad.
