The 22-year-old France international has signed a five-year deal with the Premier League champions.
He becomes Chelsea’s second major summer signing after they brought in defender Antonio Rudiger from Roma.
The 22-year- old has cost the Blues £40m- some £10m less than Fernando Torres in 2011.
He told the club website: “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.”
Chelsea technical director Michael Emenalo said: “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.”
The imposing defensive midfielder will add considerable power and energy to Antonio Conte’s side, but his signing raises further doubts about the future of Nemanja Matic.
Bakayoko, who joined Monaco from Rennes in 2014 and made his senior France debut in a friendly loss to Spain earlier this year, is Chelsea’s third summer signing.