Bakayoko teased his move to Stamford Bridge for several days but finally had a medical in London yesterday and finalised the move.
He becomes Chelsea third signing of the summer following the arrivals of Willy Caballero and Antonio Rudiger.
Bakayoko 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 and alongside so many great team-mates.”
Technical director Michael Emenalo added: “Tiemoue was outstanding as Monaco emerged as one of Europe’s best sides last season and we are delighted to welcome him to Chelsea.
“Despite his young age he already has plenty of experience as a French title winner and having competed in the latter stages of the Champions League, we believe he will add considerable quality to our squad.”
Bakayoko’s signing is likely to push Nemanja Matic towards Manchester United.
Matic was given permission to miss Chelsea’s pre-season tour of the Far East having been linked with a £40m move to United this summer.
