In an open letter to supporters, Ozil said “Arsenal fans will forever remain in my heart”.
The German has also thanked Gunners technical director Edu for helping to reach “a dignified solution” to the end of his time at Emirates Stadium.
Ozil has signed for Fenerbahce on a free transfer after coming to an agreement with Arsenal over the early termination of his £350,000-a-week contract.
Ozil wrote: "It is difficult for me to put into words the love I feel for the club and the fans. How could I possibly describe eight years of gratitude in a single letter?
“I will be a Gunner for life - no doubt about that. 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.
"Arsenal is a club of class and prestige, something that I felt every time I walked on to the pitch.
“Players, staff and management always come and go - but the club's values and fans will remain forever.
"The principles of class, respect and dignity must never be forgotten. It is the responsibility of every single person from the club to make sure they carry out their job in the name of these values.
“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.”
Mikel Arteta said Ozil’s achievements at Arsenal are “undisputed”.
Ozil, who joined Arsenal from Real Madrid for £42.5million in 2013, won the FA Cup four times during his time at Emirates Stadium.
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.”