The 22-year-old France international has signed a five-year deal with the Premier League champions.
Bakayoko, who will wear the number 14 shirt at Chelsea, said: “I am very happy to be here and to join this great team.
“I have grown up watching Chelsea. Signing was the natural thing for me because it is a club I loved very much in my childhood.
“I am now looking forward to evolving under this fantastic coach [Antonio Conte] and alongside so many great team-mates.”