The England defender has been linked with an exit from the Etihad Stadium throughout the summer after struggling to establish himself as part of manager Manuel Pellegrini’s first team.
Richards is part of a group of players, including Matija Nastasic - who is being linked with Everton - Scott Sinclair and John Guidetti who have been left out of Pellegrini’s 22-man squad for this season.
The 26-year-old was heavily linked with a move to West Ham and was also reportedly a target for fellow Premier League sides Liverpool and Sunderland earlier this summer.
The terms of the deal taking Richards to Fiorentina have not been disclosed by either club, but City have signed two players from the Serie A side in the last two seasons - Nastasic and Stefan Jovetic.
Last month, Pellegrini confirmed Richards turned down an offer to renew his contract at City.