Earlier this month, Wolves took up their option to sign Afobe after a successful loan spell from Bournemouth, but it quickly began to emerge that the player could be leaving Molineux for the bet365 Stadium.
Both clubs have now confirmed that a transfer has been completed for an undisclosed fee, with reports suggesting that Stoke have paid in the region of £12m to secure the signature of the 25-year-old.
Stoke boss Gary Rowett told the club's official website: "If there's one signing you want to make to get you out of the Championship Benik is that kind of player.
"The club have worked incredibly hard to make the signings of Benik and [Oghenekaro] Etebo happen and I think it shows how quickly we want to hit the ground running and the type of players we want to bring to the club. Getting those two in the building is a fantastic start."
During the second half of last season, Afobe netted six times in 16 outings to help Wolves win the Championship title.