Bridges made his name as a youngster at Sunderland before a £5million move to Leeds in 1999 but has been troubled by injury ever since.
He told the Sunderland Echo: "I am very sad. I would have loved to have stayed at Sunderland and I know I still have a lot to offer the club, but that is not the way the manager sees it.
"And if you are not wanted, you have to accept that it is better to get off and go somewhere where you are."