The French youngster, 19, has been immediately loaned back to the Ligue 1 club until the end of the season.
Zouma has been one of Chelsea's top targets in the transfer window, and Jose Mourinho sees him as a long-term replacement for the ageing John Terry.
The strong centre-back has represented France at all youth levels, and has put pen-to-paper on a five-and-a-half year contract.
Soccer Headlines
CONFIRMED: Kurt Zouma signs for Chelsea in £12.5m move
The Express | Jan 31