Sarr, 21, left Nice at the end of his contract after playing for the club since the age of six.
His availability led to huge interest and the likes of Arsenal and Torino were linked with the France under-21 international.
But it is Chelsea who have won the race, convincing Sarr to move to Stamford Bridge.
According to Gianluca Di Marzio, Sarr has agreed a five-year deal and will undergo a medical soon.
The likelihood is that Sarr will be loaned out by Chelsea, who are also bringing in Thiago Silva on a free transfer.
Sarr’s move to Chelsea has now been confirmed by the club.
He has signed a five-year deal at Chelsea and they will be sending him out on loan for the 2020-21 season.
Welcome to Chelsea, Malang Sarr! ✍️
— Chelsea FC (@ChelseaFC) August 27, 2020