"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," the 28-year-old told City's official site.
"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."
Bridge had a frosty spell with Chelsea, playing second fiddle for England's first-choice left-back Ashley Cole.
But the former Southampton man is hopeful he could regain match practice with Mark Hughes' side.
"I’m just looking forward to getting out and playing some regular football," said Bridge.
"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."