Ozil brings to an end a seven-and-a-half year stay in North London, having joined from Real Madrid for a then club record fee of £42.4m in the summer of 2013.
The 32-year-old former Germany international won three FA Cups with Arsenal but has not played for the club since March 2020.
Ozil was frozen out of the Arsenal set up for the first half of the 2020/2021 season despite being the club’s highest earner.
He made 254 appearances in all competitions for Arsenal, scoring 44 goals and providing 71 assists.
In a goodbye message to the Arsenal fraternity, 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."
Arsenal manager Mikel Arteta added: "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."
