The 33-year-old leaves the Yellow Canaries after just 18 months with the club, who have confirmed that they have terminated his contract.
A brief statement on Fenerbahce's official website read: "It has been agreed that the contract between our club and Mesut Ozil will be terminated by mutual agreement.
"It presents to the public; We wish Mesut Ozil success for the rest of his career."
Ozil did not feature for the Turkish top-flight side for the final three months of the 2021-22 campaign following a bust-up with interim boss Ismail Kartal.
Jorge Jesus has since taken the reins at Fenerbahce but the 92-cap Germany international is not part of his plans, which has resulted in the termination of his contract.
Istanbul Basaksehir has now confirmed the arrival Ozil on a free transfer via Twitter, and the playmaker has become the club's ninth signing of the summer window after Leo Duarte, Ahmed Touba, Mounir Chouiar, Patryk Szysz, Zaglebie Lubin, Lucas Biglia, Fatih Karagumruk and Alper Karaman.
Ozil made 36 appearances for Fenerbahce across all competitions, scoring eight goals and providing three assists.