The centre-back signed a four-year contract with the Blues.
In his three years with the Italian side, the Senegalese player made 317 appearances.
His arrival at the Bridge follows the departures of two defenders in free transfers.
"I'm very happy to be a part of this team."
It's a big team in the world and I always dreamed of playing in the premier league. We didn't make it, but we were the first to get me. I accepted it because they really wanted me to join them in the premier league.
They made my choice easier when I talked to them.
He captained the team to victory at the Africa Cup of Nations in 2021.
He is the second player to join the club since the takeover by Todd Boehly.
Boehly said that they were excited to be welcoming one of the world's elite defenders to the club.
Kalidou brings a wealth of experience and attributes that will benefit our squad and the club as a whole.