The striker is likely to move to the bet365 Stadium for around £12million and help spearhead the Potters' promotion challenge.
He joined Wolves on Friday after they triggered an option in his loan deal to buy him from Bournemouth for £10million.
Afobe scored six goals in 17 appearances for Wolves after returning on loan in January as the club won the Sky Bet Championship title.
The 25-year-old initially left Molineux for Bournemouth for £10million in 2016 having scored 22 goals in 46 league games.
He managed 11 goals in 70 games for Eddie Howe's side but struggled to pin down a regular spot, making just five league starts in the first half of the season before heading back to Molineux.
Afobe started his career at Arsenal but did not make an appearance for the Gunners.
Stoke were relegated from the Premier League last season and have since appointed Gary Rowett as their new boss.
He is also said to have seen a bid for West Brom winger James McClean rejected as the Potters rebuild in the second tier.
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