World Cup winner Ozil, once Arsenal's record signing, had been excluded from Mikel Arteta's first-team plans this season and departs after seven and a half years with the Premier League club.
The former Germany midfielder was under contract until the end of the current campaign but reached an agreement for an early termination, clearing him to sign elsewhere.
Fener have now confirmed the arrival of Ozil, with Arsenal announcing the playmaker's departure on their official website.
In a statement in the Gunners' announcement, Ozil said: "I'd like to thank the club for this amazing journey over the past seven-and-a-half years.
"The support I have felt from the team and fans during my time here has been truly incredible and something I will always be grateful for.
"Together we won trophies for the first time in years and created memories that will last a lifetime.
"The Arsenal fans will forever remain in my heart."
He was a key part of Arsene Wenger's squad that finished second in the 2015-16 Premier League season, while he also started in the FA Cup final triumphs in 2014, 2015 and 2017.