1030 GMT July 23 2017
The 22-year-old France international signed a five-year deal with the Premier League champion, BBC reported.
He becomes Chelsea's second major summer signing after the Blues brought in defender Antonio Rudiger from Roma.
Bakayoko joined Monaco from Ligue 1 rival Rennes in 2014 and made his France debut in a friendly defeat by Spain in March this year.
He was part of the Monaco squad that reached the Champions League semifinals last season, going out of the competition to Juventus.
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."
“Tiemoué was outstanding as Monaco emerged as one of Europe’s best sides last season and we are delighted to welcome him to Chelsea,” said Michael Emenalo, the champion’s technical director. “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.”