The 32-year-old former Southampton and Chelsea defender, who spent a loan spell at Brighton last season, has signed a one-year deal to become Nigel Adkins' first signing since taking charge at the Madejski.
"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 told the club's official website.
"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 added: "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, who played 36 times for his country, made 42 starts at this level with Gus Poyet's Brighton last season and his displays earned him a place in the npower Championship Team of the Year.