The England international, 34, who has signed a three-year deal, said: "It's great to be back. The one thing I can guarantee is goals."
"It was an easy decision, joining a top team with a top manager," added Defoe who scored 15 league goals last season.
Cherries boss Eddie Howe said Defoe's signing is a "huge moment for the club".
"We want to bring players here who can have a big impact on our continued rise and we believe Jermain fits that as a natural, proven goalscorer," added Howe.