The 20-year-old has joined Milan on a "two-year loan with obligation to buy", meaning that he will technically be on loan with the Italian giants until the summer of 2019, before his move from Atalanta BC becomes permanent.
Kessie is believed to have turned down interest from the likes of Manchester United and Chelsea to sign with Milan, and the Ivorian international has said that he is "very happy" to have made the move to Vincenzo Montella's side.
"I have to thank everyone, my agents, the team, and I am very happy to be part of this squad," Kessie told Milan TV.
"I chose Milan because I like the project. There are new directors who explained everything very well and that was really pleasing. I spoke to the coach, who told me to come to Milan because I could become a champion here."
Kessie scored six times and registered four assists in 30 Serie A appearances for Atalanta last season.