The German attacking midfielder completed a free transfer to Fenerbahce on Sunday, ending his seven-and-a-half year stay in north London.
"Mesut's achievements at Arsenal are undisputed. It was a privilege to play alongside him and, more recently, coach him," he told the club's website.
"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."
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