Ozil, 32, spent seven-and-a-half years at Arsenal after joining from Real Madrid in 2013 for a then-club record fee of £42.5 million and went on to win the FA Cup three times. He also helped the club reach the Carabao Cup final in 2018 and the Europa League final in 2019, as well as making 184 Premier League appearances.
Arsenal manager Mikel Arteta said: "Mesut's achievements at Arsenal are undisputed. It was a privilege to play alongside him and, more recently, coach him. His creativity and vision led to many goals during his time in the Arsenal shirt.
"Mesut was at the heart of many great moments for this club over the years, including those three FA Cup final wins. These successes will always be part of our history. We thank Mesut and wish him all the best with Fenerbahce."
Despite being Arsenal's highest-paid player on a contract worth £350,000-a-week, Ozil saw his playing time limited under Arteta and he was not included in the squad registered to play in the 2020-21 Premier League and Europa League.
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. I'd like to thank Edu Gaspar for helping bring about a professional and dignified solution in the past few days, and I wish everyone at the club the best in their attempt to continue to bring Arsenal back to the top, where we belong."
The 2014 World Cup winner started Arteta's first 10 Premier League games in charge after replacing Unai Emery as Arsenal boss in December 2019, but has not been considered since refusing to take a 12.5% pay cut along with the majority of the first-team squad after failing to receive information over how the money would be spent.
His last appearance for Arsenal came in the 1-0 win against West Ham on March 7.
Ozil has since donated a greater amount to helping London charities including social project "Ozil's Warmer Winters" which aimed to provide 50,000 healthy meals and 10,000 gift packages to people in need over Christmas.
His first three years at the club saw his best form, equalling Thierry Henry's record of 19 Premier League assists in 2015-16.
Ozil, who was in the final six months of his Arsenal contract, was also linked with a move to MLS side D.C. United as well as clubs in Asia and Qatar.