The 22-year-old striker has signed a four-and-a-half year deal with the Cherries for a reported fee of more than £8million.
Former Arsenal youngster Afobe departs Wolves having only arrived at the Molineux in January 2015 during which time he managed to score 23 goals in 48 appearances.
Upon his move to Dean Court, to link up with Eddie Howe's side, Afobe told the Dorset club's official website: "I'm delighted.
“It's been a long time coming and I am just very thankful the manager has given me this chance and opportunity to be at this Premier League club and I can't wait to get going.
"I have done a lot for someone that's only 22. I've had injuries, I've been out on loan to six different clubs, so I've played for a lot of different clubs in my young career so far.
"I've learned a lot definitely - good things and bad things - and I'm just going to take it all on board and keep improving while I'm here at Bournemouth.
“The manager here is a young manager so he obviously understands how young players think. He just wants to get the best out of me and that's what I want to do."
Looking forward to putting this shirt on and meeting all my new team mates tomorrow. Thanks for the messages #COYCpic.twitter.com/Xrdqtd8klQ
— Benik Afobé (@Afobe_) January 10, 2016