Basaksehir finished fourth last season, eight points behind second-placed Fenerbahce.
Fenerbahce released a statement on Wednesday which read: "It has been agreed that the contract between our club and Mesut Ozil will be terminated by mutual agreement.
"We wish Mesut Ozil success for the rest of his career."
Ozil, who joined the Turkish giants on a free transfer from Arsenal last year, still had two years to run on his contract.
The midfielder hadn't played for the club since March following a row with then-interim boss Ismail Kartal.
The 33-year-old reacted on social media on Wednesday to the announcement and said: "One of the things that makes life is that it is full of uncertainties.
"Our plans, desires and wishes may not always go in the direction you want them to. I wanted to achieve success by getting more chances to play in the Fenerbahce jersey, which has always been my childhood dream.
"I would like to thank the Fenerbahce community and fans for the great support they have shown me."
The former Germany international only played 37 times across his season-and-a-half in Turkey.
Information from Reuters was included in this report.