Zouma, 22, leaves Stamford Bridge in search of first-team football having struggled to break into Antonio Conte's side last season following his return from a serious knee injury. The former Saint-Etienne defender suffered a ruptured anterior cruciate ligament during a Premier League match against Manchester United in February 2016, returning to first-team action at the start of the year.
With Conte's back-three of Cesar Azpilicueta, David Luiz and Gary Cahill thriving, he was unable to force his way into contention, making just three Premier League starts and a further three in the FA Cup.
Zouma would appear to remain in the club's long-term plans given the length of his new deal, however, and will get the chance to recapture his best form at the Britannia Stadium.
Potters boss Mark Hughes described his latest acquisition as "undoubtedly one of the most talented young defenders in the game", adding his side have fought off plenty of competition to land him.
"There has been huge interest in him, from both home and abroad, so we are incredibly pleased that he has decided that Stoke City is the right place for him to continue his development," Hughes said.
Chelsea will keep a watchful eye over the defender they spent £12m on in 2014, with Blues' technical director Michael Emenalo adding: "It is fantastic Kurt has chosen to commit his future to Chelsea. He has shown his talent since joining us three years ago, and has returned from a serious injury with a fantastic attitude.
"Now he has the opportunity to play regularly in the Premier League and we will be monitoring his progress closely while he is at Stoke."
The arrival of Antonio Rüdiger at Stamford Bridge from Roma meant Antonio Conte had one more option at his disposal ahead of Zouma. 21-year-old Andreas Christensen could also be in first-team contention, although the Denmark international will find himself in no shortage of suitors should the club decide to move him on following two superb seasons in Germany with Borussia Monchengladbach.