Richards arrived in Florence on Monday morning to undergo a medical before completing his switch to the Serie A outfit.
As part of the agreement, Fiorentina will hold an option to make Richards' move permanent next summer.
The 26-year-old right-back had turned down an option to sign a new contract with City earlier this year and was looking for a fresh challenge having fallen behind Pablo Zabaleta and Bacary Sagna in the pecking order.
Richards has made almost 250 appearances for the Blues outfit since making his debut with the club in 2005.
Source : PA