The France midfielder will now head to London to undergo a medical tomorrow and complete his move.
Chelsea have been trying to get the deal done for weeks and have finally reached an agreement with the club.
They will play £39.8m plus add-ons for the 22-year-old, who will sign a five-year deal.
Bakayoko’s brother Abdoulaye hinted the deal was close earlier today by posting an image with a black background along with the caption CFC, accompanied by the blue dot and strong arm emojis.
Fans have already been bombarding the Blues twitter account, demanding the 22-year-old’s signing be announced by the club.
And now they will get their way despite late interest from Manchester United.
Chelsea boss Antonio Conte made Bakayoko his top midfield target to play alongside N’Golo Kante.
And his arrival is likely to see Nemanja Matic join Manchester United and Nathaniel Chalobah leave the club with Watford interested.
Despite winning the title in his first season Conte has been desperate to add new players in key areas and Bakayoko follows defender Antonio Rudiger and new back up goalkeeper Willy Caballero.
The Italian is still keen to sign another wing back and is in talks with Real Madrid over a deal for Danilo with Alex Sandro’s move from Juventus dragging.
Conte also needs a centre forward to replace Diego Costa having missed out on Romelu Lukaku.
The Blues have been offered Pierre-Emerick Aubameyang for £70m but are keen on Alvaro Morata and Andrea Belotti.
