Milan did not specify the transfer fee or the length of the contract but British media reported that the club would pay around one million euros ($ 1.2 million) for the player, who is expected to sign a two-year deal.
World Cup-winner Giroud scored 39 goals in 119 games in all competitions for Chelsea and helped the London outfit claim the Champions League, Europa League and FA Cup after joining them from Arsenal in 2018.
The 34-year old thanked Chelsea’s fans, players and coaches for “special moments” before his switch away from the Premier League club.
“To all the Blues, to my team mates, to all my coaches, to the whole club, a huge thank you for these special moments,” Giroud tweeted.
“I’m starting a new journey with a light and happy heart. Our victories in the FA Cup, Europa League and Champions League have been magnificent.”
Giroud joined Chelsea from Arsenal in January 2018 and had a year left on his contract at Stamford Bridge.
He started only eight Premier League games for Chelsea last season following the arrival of German forwards Kai Havertz and Timo Werner.
He was part of France’s Euro 2020 campaign where the world champions were knocked out by Switzerland in the last-16.
In June, Milan signed Chelsea’s Fikayo Tomori on a permanent transfer after the defender spent the second half of the 2020-21 season with the Italian side on loan.
Milan, who finished second in Serie A last season, begin their 2021-22 league campaign away to Sampdoria on Aug. 22.