The 25-year-old won the Premier League with the Gunners when he was just 18, but the France international has not won any silverware with the north London side since.
"After spending eight years with Arsenal it would have been easy to sign a new contract to stay there because they're a fantastic club that will always be challenging for trophies,” he said.
"But it got to a point for me where I didn't want to just challenge for the titles only to be disappointed in the final weeks of the season. I wanted to play for a club that would win them.
"I joined City because I felt that this was a club ready to win important trophies over the next few years."
Clichy made 187 appearances for Arsenal after joining from French side Cannes in 2003.