Bridge has signed a one-year contract 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 next season,” Bridge said.
“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.”
Reading went down from the top flight last season along with QPR and Wigan Athletic.
Rs boss Harry Redknapp said this week that he was hopeful of making Bridge his first signing of the summer, but he has been beaten to the punch by Royals boss Nigel Adkins.
The Daily Mirror reported on Friday that Redknapp could walk out of Loftus Road if he missed out on the experienced former Southampton, Chelsea and Manchester City defender.
Reading 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.”
Bridge, 32, has more than 300 Premier League appearances and 36 England caps to his name.
He spent last season on loan at Brighton from Manchester City, but the Seagulls lost in the play-offs.