Bailly, who moved to Old Trafford from Villarreal for £30 million ($37m) in 2016, was told ahead of the new season he was not part of Erik ten Hag's plans and had been training with the reserves.
He signed a new contract in April 2021 and despite having a year left on his deal, the 29-year-old, who spent last season on loan at Marseilles, has been allowed to move to Besiktas for free.
The Ivory Coast international leaves having made 113 appearances, scoring one goal. Since signing his last deal at United, Bailly made only 13 appearances in all competitions, starting just six games in the Premier League.
Sources have told ESPN that United are also hoping to offload Donny van de Beek before the close of the transfer windows in Turkey and Saudi Arabia.
Van de Beek joined United from Ajax for £35m in 2020 but last season was restricted to just 10 appearances in all competitions.