The 37-year-old's move comes just weeks after he penned a new deal with Lee Johnson's side and ends a three-year stay at Ashton Gate, where he scored 30 goals in 107 league appearances.
"I'm really pleased to get the move over the line and can't wait to get going," Wilbraham told the Bolton website. "I've joined the club at an exciting time following their promotion back to the Championship earlier this year and I'm really looking forward to introducing myself to the fans.
"I feel I bring a lot of experience to the table and I'm ready to give my all for Bolton Wanderers in what should be an exciting season for us."
Speaking about Wilbrahm's exit, Johnson said: "It's difficult because we didn't want to lose Aaron but it's a fantastic deal that he has been offered by Bolton. He's been away from his family when he's lived in Bristol and this now gives him a chance to be back with his wife and daughter. It also gives him the opportunity to kick on with the playing side of his game, which he really wants.
"Obviously for us, we were talking about Aaron with non-playing responsibilities. Every player wants to play as high as he can and for as long as possible.
"With the deal that is on offer from Bolton, the playing opportunities and the fact he can get home to his family, it was very difficult to stop him taking that and standing in his way. He moves on with our best wishes and we thank him for everything he did for this football club."
During his playing career, Wilbraham has achieved five promotions, including two into the Premier League with Norwich City and Crystal Palace.