The 21-year-old would be released after leaving Nice at the end of his contract this summer and had been in line with Barcelona and Arsenal.
However, the Frenchman has now put the pen on paper on a five-year contract that will keep him at Stamford Bridge until 2025, the first of his years on loan.
“The opportunity to point out one to Malang that we couldn’t miss,” manager Marina Granovskaia told Chelsea’s official website.
“It’s a wonderful prospect and we’ll look at it a lot during your loan period, hoping you’ll be back to Chelsea soon. We are very pleased to welcome you to the club today.”
The centre-back, also able to do it from the left, climbed a ladder in Nice and played 119 times with the first team.
Sarr becomes Chelsea’s time signing so many days after Ben Chilwell’s arrival on Wednesday, and the fourth from the window, with Hakim Ziyech and Timo Werner also joining.