Left-back Bolingoli has left the Scottish champions on loan initially, but the Super Lig switch could lead to a permanent deal.
Celtic manager Neil Lennon confirmed this week that the club had imposed the maximum fine allowed on Bolingoli after he left the Hoops embarrassed in early August.
✍ 8.15 ⏰— İstanbul Başakşehir (@ibfk2014) September 13, 2020
🎶 ...dillere dolansa, destan olsa bu sevda! pic.twitter.com/vQZVfR1HjX
The 25-year-old Belgian travelled to Spain without Celtic's knowledge and did not follow coronavirus quarantine rules when returning to Scotland, going on to play in an August 9 match against Kilmarnock.
Scotland's First Minister Nicola Sturgeon expressed dismay over the episode, and Celtic at the time said: "It is difficult to imagine a more irresponsible action in current circumstances and we find it beyond explanation."
Two Celtic matches had to be postponed because of Bolingoli's actions, and immediately his future at Parkhead looked bleak, despite him issuing an apology.
Confirmation of his departure on Sunday came as no surprise.
Istanbul Basaksehir announced on their website: "Our club has loaned Belgian football player Boli Bolingoli-Mbombo for a year with the option to buy."