“Our club has signed a one year contract with the option of another year with Mesut Özil,” Basaksehir said in a statement.
Basaksehir is known for its close ties with Turkish President Recep Tayyip Erdogan, who was best man at Ozil’s wedding in 2019 to a former Miss Turkey, Amine Gulse.
Ozil, 33, split with Fenerbahce with two years of his deal still to run.
He joined the Istanbul side less than a year and a half ago but has been excluded from the first team since the end of March following a dispute.
New manager Jorge Jesus made it clear he would not rush to overturn that decision when he took up the post at the beginning of June.
Ozil arrived at Fenerbahce in January 2021 from Arsenal, where he had been excluded from the Gunners’ Premier League and Europa League squads that season. His last game for the London club was March 2020.
Ozil joined Arsenal from Real Madrid in 2013 and lifted the FA Cup on three occasions under then-coach Arsene Wenger.
The 2014 Germany World Cup winner of Turkish origins ended his international career after what he described as “racist” attacks following the holders’ first-round exit at the 2018 World Cup.
He had come in for strong criticism in Germany after posing for a photograph with Erdogan in 2018.