the 22-year-old will have a medical later this week ahead of his move to the Premier League champions.
The deal had been slightly delayed as Bakayoko has been recovering from minor knee surgery that he underwent at the end of last season.
Bakayoko helped Monaco win the French title last season for the first time in 17 years, making 51 appearances as Leonardo Jardim's side also reached the semi-finals of the Champions League.
His arrival at Stamford Bridge could pave the way for Nemanja Matic to leave the club.
Manchester United have identified the Serbia international as a target as they look to strengthen their defensive midfield options.
But Chelsea are understood to be reluctant to sell Matic to United after Jose Mourinho secured the signing of Romelu Lukaku ahead of them.