The Wales international joined Bolton in a £2m move from Hull City four years ago and went on to make over 100 appearances for Wanderers.
He was a regular starter under Owen Coyle and Dougie Freedman last season, making 35 appearances.
A club statement read: "Bolton Wanderers would like to thank Sam for his services to the club and wishes him well in his future endeavours."
Ricketts has now signed a two-year deal with Wolves, who are looking for a quick return to the Championship after their relegation last season.
The 31-year-old is reunited with Kenny Jackett at Molineux after enjoying considerable success under him at Swansea City.