Clichy has signed a four-year contract and joins City for an undisclosed fee, believed to be around £7million.
"I am really happy to be joining such a great club," he told City's official website.
"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."
"When I first came to England, it was Kolo Toure and Patrick Vieira who took me under their wing and really looked after me," added Clichy.
"Kolo would pick me up and drop me at home and his wife used to cook meals for me. Patrick was always there to offer me advice so it's wonderful to be back and at the same club they are at."