Pulisic has already trained with his new team and head coach Stefano Pioli
Pulisic, 24, has signed a four-year deal with the Serie A side, with the option of a further year.
He scored 26 goals in 145 games at Chelsea and played in the 2021 Champions League final win over Manchester City.
However Pulisic became surplus to requirements at Stamford Bridge, scoring only once in his final season.
"It was a difficult last few season with Chelsea. For whatever reason I wasn't getting the opportunities I wanted," he told a news conference for his unveiling.
"For me it's a brilliant opportunity to step away, get a fresh start and play for a big team like this."
Chelsea released a statement confirming the transfer, saying: "We wish Christian well and thank him for all his contributions during his time at the club."
He joined Chelsea from Borussia Dortmund in a £57.6m move in 2019 that made him the most expensive player from North America.
The Pennsylvania native has also been capped 60 times by his country.
His switch to Serie A sees him linking up with former Chelsea team-mate Ruben Loftus-Cheek, who has also joined Milan this summer.
Chelsea have parted ways with several established first-team players this summer.
The departures have included Kai Havertz moving to Arsenal, Mateo Kovacic joining Manchester City and Mason Mount making the switch to Manchester United.
Cesar Azpilicueta has joined Atletico Madrid on a free transfer, while other exits have seen Kalidou Koulibaly, Edouard Mendy and N'Golo move to the Saudi Pro League, joining Al-Hilal, Al-Ahli and Al-Ittihad respectively.
-- Courtesy of BBC Sport