The 22-year-old joined Antonio Conte's Chelsea on a five-year contract for a reported fee of up to £39.7 million ($51.98m, 45.3m euros) after helping the principality side win the Ligue 1 title last season.
"I am very happy to be here and to join this great team," Bakayoko said in a statement on the Chelsea website.
"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."
Bakayoko was one of the stars of Leonardo Jardim's youthful Monaco outfit that surprisingly beat Paris Saint-Germain to the French title in May, while also reaching the Champions League semi-finals.
The completion of the deal is a boost for Chelsea manager Conte, after he missed out on former Everton striker Romelu Lukaku to Manchester United.
There had been speculation United might try and stymie the bid for Bakayoko just as they did with Lukaku, as they broke the record for a deal between British clubs of £75m to prise him away from Goodison Park on Monday.
However, Bakayoko, whom Monaco will make a tidy profit on having signed him from Rennes for £7m in 2014, had always made it clear that Chelsea was his preferred destination.
"Tiemoue was outstanding as Monaco emerged as one of Europe's best sides last season and we are delighted to welcome him to Chelsea," said the Blues' technical director Michael Emenalo.
"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 made his international debut in a friendly defeat by Spain in March, and will team up with compatriot N'Golo Kante in the Chelsea midfield.
His arrival also paves the way for the possible departure from Stamford Bridge of Serbian Nemanja Matic.
However, Chelsea are not keen to sell him to the original suitors Manchester United, as relations between the two rivals have cooled considerably since the Lukaku affair.
Bakayoko is Chelsea's third major signing of the close season so far, following the arrivals of goalkeeper Willy Caballero from Manchester City and Germany centre-back Antonio Rudiger from Roma.
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.com.gh
