Bridge said: "I'm delighted to sign for Reading and excited to be joining a team that is going to be looking for promotion next season.
"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.
"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."