The Frenchman became a free agent when his Nice contract expired on 30 June and Chelsea has said he will spend the 2020-21 season out on loan.
He is Chelsea’s fourth signing of the summer and their second in two days after the arrival of left-back Ben Chilwell, 23, from Leicester.
Earlier in the year, the Blues signed winger Hakim Ziyech from Ajax and striker Werner from RB Leipzig.
Chelsea director Marina Granovskaia said: “The opportunity to sign Malang was one we could not miss. He is a tremendous prospect and we will be monitoring him closely during his loan period.”