The two-and-a-half-year loan deal, which is the remainder of his contract at Barcelona, still allows the Catalans to sell Turan during that period if a club makes an offer for him.
Turan's new club Basaksehir have risen fast over the last two seasons to rival the established Istanbul triumvirate of Besiktas, Fenerbahce and Galatasaray and lead the Super Lig by a point.
Turan, who turns 31 at the end of the month, joined Barca for €35 million in 2015 during an election campaign, a signing made by president Josep Maria Bartomeu and backed by Luis Enrique, the club's coach at the time.
Basaksehir will pay Barca in variables dependent on a number of factors, including appearances and goals, as well as the team's success with Turan at the club.
Although Turan moved from Atletico Madrid to Barcelona in the summer of 2015, he made his debut in January 2016 due to a Federation Internationale de Football Association transfer ban on the Catalan side.
The midfielder claimed six titles with Barcelona: one La Liga, two Copa del Rey, one Spanish Super Cup, one Club World Cup and one European Super Cup.