The 25-year-old had a year remaining on his deal at the Emirates Stadium but after failing to agree an extension has completed his move to The Blues for a reported £7 million.
Clichy, Roberto Mancini's first signing of the summer transfer window, will compete for the left-back birth with Pablo Zabaleta and Aleksandar Kolarov, who vied over the position for most of last season.
Clichy said: "I’m really happy to be joining such a great club. I hope I can add to the quality we already have here because we have a fantastic squad who I believe will continue to get better.
“I can’t wait to get started and I think anything is possible with this team.”
During his eight year stay at Arsenal, Clichy made 264 appearances for the Gunners and became the youngster player to win a Premier League winners medal in 2004 during the club's unbeaten league season.
While Arsenal continue to go through a trophy drought stretching back to 2005, City have recently captured the FA Cup and qualified for the Champions League last season, finishing third ahead of the north-Londoners in the Premier League.
On his departure, Arsene Wenger said: "We would like to thank Gael for eight years of terrific service to Arsenal, during which time he gave absolutely everything for the Club.
"He has grown and developed so much since joining us in 2003, and has been a crucial part of the team over recent seasons. Gael leaves with our respect and best wishes. We wish him the very best for his future career."