The 31-year-old was not offered a new contract at the Etihad at the end of the 2016-17 season.
The club have confirmed on social media that he will have a medical before signing a contract on Friday.
Clichy joined City from Arsenal in 2011, twice winning the Premier League title and EFL Cup with the club.
The terms of the deal have not been revealed, but reports in Turkey suggest the former France defender will be paid 3m euros (£2.6m) per season in a three-year deal.
Clichy will team up with former City and Arsenal striker Emmanuel Adebayor who signed for Istanbul Basaksehir in January.
Adebayor scored six league goals as the side finished runners-up in the Turkish Super Lig last season.
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