The powerful French U-21 international, who made his first-team debut at the age of 16, will be loaned back to Saint-Etienne until the end of the season. Zouma was part of the france side that won the FIFA U-20 World Cup Turkey 2013.
Chelsea did not disclose how much they had paid to sign Zouma, but reports in the British media and in France suggested that the transfer fee was around £12 million. Zouma is Chelsea's fourth signing of the January transfer window, after Nemanja Matic, Mohamed Salah and Bertrand Traore.
Manager Jose Mourinho said that Chelsea had moved quickly to sign Zouma in order to fend off interest from other clubs, but he revealed that the teenager may be immediately loaned out when he arrives at the end of the season.
"If we don't do it now, probably we can't do it in the summer because other clubs were also very strong on him," Mourinho told reporters during his weekly press conference. "So we did it. Now he stays at Saint-Etienne, pre-season he will join us. We will see if it is to stay or if it is to go on loan."
Upon returning to Chelsea last year, Mourinho spoke of his desire to leave a long-term legacy at Stamford Bridge, and he congratulated the club for signing another highly regarded young player. "He's another young player in the profile of some Chelsea have signed in the last couple of years," Mourinho said.
"We liked the profile, we think he's very much adapted to the Premier League. He is a young player for a position where we also need the future. He's a player with big potential, physically ready. One thing is to be physically ready, another thing is to be tactically ready. Well done Chelsea."
Zouma, who had also been linked with Inter Milan and Monaco, recently completed a 10-match ban for a challenge that fractured the leg of Sochaux's Thomas Guerbert during a Ligue 1 match last November.