The striker signs a four-and-a-half year deal with the Premier League club after they reached an agreement with Wolves
And, following a successful medical, the transfer has been finalised, with the attacker signing a four-and-a-half year deal.
READ MORE | Hiddink: Oscar-Costa clash shows fight and emotion
"We are absolutely delighted to secure the signature of another undoubted talent in Benik Afobe," Bournemouth chief executive Neill Blake told the club's official website.
"It has been difficult to miss Benik's outstanding progress as a player, firstly with MK Dons and then Wolves, where he has been a consistent threat in front of goal.
"His pedigree as an Arsenal academy product must also not be underestimated.
"Thank you to Jez Moxey and Wolverhampton Wanderers, who have been a pleasure to deal with throughout negotiations.
"We look forward to seeing Benik in an AFC Bournemouth shirt soon."
Afobe, who joined Wolves from Arsenal in January last year, scored 13 goals for the Midlands club last term.
The 22-year-old has already found the net 10 times this campaign and will look to make a similar impact for a Bournemouth team that is four points above the Premier League relegation zone.