The 19-year-old was signed by Jose Mourinho in January in a £12m deal, but he was immediately loaned back to Saint-Etienne for the remainder of the campaign.
Despite reports suggesting that the central defender will leave Stamford Bridge on a temporary basis, Zouma has insisted that he is concentrating on impressing Mourinho.
"I told him, yes. I am very excited, I am very happy to come to the club," Zouma told members of the media. "He's the best manager in the world and I'm so happy to be able to work with him.
"Initially it will be a period of adaptation but I hope I can improve as a player, get into the team and just play as many matches as possible."
Sunderland were recently linked with a loan bid for Zouma.