The 22-year-old has been on the Blues' radar for most of the summer, while he was also previously being linked with a move to Premier League rivals Manchester United.
Bakayoko arrived in London earlier this week to finalise personal terms and undergo a medical, however, paving the way for a transfer reportedly worth around £40m - the second-highest fee ever paid by the West London outfit to sign a player.
A Ligue 1 title winner with Monaco last season, Bakayoko is the latest star name to depart the principality club, trying his luck in English football for the first time in 2017-18 following spells with the Monegasques and Rennes.
Speaking to his new side's official website, the recently-capped France international 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 teammates."
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."