Bakayoko, 22, is a tall, strong and quick central midfielder who was instrumental in Monaco’s Ligue 1 triumph last season, as well as their impressive run to the Champions League semi-finals.
He recently made his debut for France in the same line-up as new team-mate N’Golo Kante, and is widely recognised as one of the best young central midfielders in European football.
Bakayoko, who has signed a five-year contract and will wear the No.14 shirt, 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.’
In possession, Bakayoko typically plays quickly and simply but has the ability to be more expansive if required, and is strong in a one-on-one situation.
Born in Paris, Bakayoko came through the Rennes academy in the north-west of France and made his senior debut in August 2013, a week after his 19th birthday.
He signed for Monaco the following summer and made almost 100 appearances for the principality side during his three seasons there, scoring five goals.