Wanderers beat off a host of clubs to agree a one-year deal, with the option of another year, with the injury-hit 25-year-old.
He ended last season on loan with Newcastle, but he started only one game, at home to Valerenga in the Uefa Cup.
Former club Sunderland and a number of other teams such as Southampton, Fulham and Leicester were all thought to be interested in signing him.
Bridges, who will officially join Bolton on July 1 when his current contract expires, cannot wait to get started with his new club.
"I was impressed by everything at Bolton, the gaffer, the stadium and the players at the club," he said. "I had a few offers from other clubs, but Sam Allardyce's influence and their status in the Premiership was a major factor in the move.
"With the likes of Jay-Jay Okocha feeding me the chances to score, it is exciting. Bolton are on the way up, considering how they finished last season, and that was a big plus point for me."