The defender has struggled for first-team opportunities with the Premier League champions and will spend the new campaign playing his trade in Serie A.
The England international made just 11 first-team appearances for Manuel Pellegrini's side during the 2013-14 season as Pablo Zabaleta held down a regular place at right-back.
And after Pellegrini revealed he could leave the club earlier in the transfer window, he has chosen to move to Serie A despite reported interest from a number of English sides including West Ham.
The 26-year-old is the Blues' longest serving player having made 245 appearances for the club since his debut in 2005, scoring 10 goals.
He becomes the second English full-back to move to Italy during the current transfer window after Ashley Cole joined Roma following his release from Chelsea.