The former England left-back was out of contract at the Etihad Stadium and joins the recently relegated Royals on a one-year deal.
Bridge, who spent last season on loan at Brighton, is Nigel Adkins' first signing since he succeeded Brian McDermott at the Madejski Stadium.
"I'm delighted to be signing for Reading and excited to be joining a team that is going to be looking for promotion from the Championship next season," said Bridge, who was also a target for QPR boss Harry Redknapp.
"I spoke to the manager and he told me about the direction he wants the team to go in. Everything we talked about was positive - and he was really positive about signing me which means a lot.
"And, from the outside, Reading look like a team who are capable of getting back into the Premier League, a team that works hard for each other.
"That is something I want to be a part of and I'm really looking forward to next season."
Director of football Nick Hammond said: "I'm delighted to have secured this agreement so early in the summer window.
"Both Wayne and his representatives have been very straightforward and professional to deal with and the player will add great experience and quality to our squad."