The goalkeeper, who played 39 games during this season’s loan spell with the Championship winners, is Bournemouth’s first signing since promotion to the Premier League.
The 35-year-old joins on an initial 12-month deal with the option of a further year.
He told the club website last month: “As soon as I came here, I saw a bunch of lads who were really working hard and they had their minds on football. In my life, I’ve never seen a group who have worked so hard and been as professional as possible.
“It’s probably the first season I’ve seen what it is to be a professional footballer from the way they are on the training ground to everything else.”
Boruc leaves St Mary’s after three years, during which time he made 50 appearances.