The defender, who has signed a four-year deal, spent the second half of the 2020-2021 season on loan with the Italian club and helped them secure Champions League football for the first time in seven years.
And Milan have decided to make the move permanent when his contract with the Blues expires on June 30.
The 23-year-old was impressive in his 22 appearances during his loan spell at the San Siro.
He helped the team keep seven clean sheets in Serie A, including five in their last five games, which saw them secure a second place finish.
The defender also made himself an instant hero by scoring in the 3-0 victory over Juventus in May.
Tomori is imposing himself with talent and determination,' Baresi said in March.
'He has shown no fear playing in a new league. He can potentially become a great champion. I hope he lives up to expectations.'