The England left-back told City's website: "I'm just excited to be here and when I spoke to the Manager yesterday he told me of the exciting times ahead at the Club.
"It's an exciting time to be at the Club with what's happening here and I'm looking forward to putting the shirt on regularly and getting out there to show everyone what I can do."
And it was a lack of first team action at Stamford Bridge that helped the former Southampton defender choose to move to the Blues as he added: "I'm just looking forward to getting out and playing some regular football.
"I haven't played that much, so I'm aiming to play on a regular basis, get my fitness up to scratch and hopefully help the team climb the table and achieve big things."
"I've spoken to Shaun already and he's already got some houses lined up for me to look at," joked Bridge.
"It's just good to be at a place where there are people I know as well and that makes things that much easier."