Potters boss Mark Hughes confirmed last week that he had a "genuine interest" in signing the 22-year-old, who only returned to action last season following a 12-month knee injury lay-off.
West Brom and Sevilla were also interested but it now seems the Potters have won the race for his signature, with the player at the club's training ground to tie up the loose ends of a switch.
Chelsea boss Antonio Conte is keen to let Zouma go out on loan to get some regular first-team football under his belt in the Premier League because his chances at Stamford Bridge next term will be further limited by the presence of recent signing Antonio Rudiger.
It is not known if the arrival of Zouma will see Hughes end his interest in signing Bruno Martins Indi, who enjoyed a successful loan at the bet365 Stadium last term.
Stoke wanted to sign him on a permanent deal this summer but have so far been unable to agree a fee with his parent club FC Porto.