The Blues confirmed the 20-year-old has signed a contract at Stamford Bridge until 2029, with the option of a further year.
The forward scored 24 goals and registered 10 assists in 65 games for Molde.
Fofana described Chelsea as the "the club of my dreams" in a short message on the club's website.
He said: "Hello dear fans, I'm here, I've arrived well and I'm very happy to sign for the club of my dreams. I'll see you soon on the pitch."
Fofana will cost a reported fee of £10.93million and becomes the latest January arrival at Stamford Bridge after Brazilian Andrey Santos and Monaco defender Benoit Badiashile.