Ba last played for Shanghai Shenhua, scoring five goals in 17 Chinese Super League appearances last year.
And the 33-year-old is returning to the Super Lig having had two previous spells with Besiktas, his new club confirming the move on Tuesday.
Istanbul Basaksehir is six points clear at the top of the table as it seeks its first-ever Super Lig title.
Ba's arrival boosts its attacking options further following the signing of former Brazil forward Robinho earlier this month.
Ex-Arsenal and Manchester City striker Emmanuel Adebayor is also on Istanbul Basaksehir's books, as well as on-loan Barcelona winger Arda Turan.