Milan did not specify the transfer fee or the length of the contract, but British media reported that the club will pay around one million euros ($ 1.2 million) for the player, who is expected to sign a contract for two years.
World Cup winner Giroud has scored 39 goals in 119 games in all competitions for Chelsea and helped the London side win the Champions League, Europa League and FA Cup after joining them from Arsenal in 2018.
The 34-year-old thanked Chelsea fans, players and coaches for the ‘special moments’ ahead of his departure from the Premier League club.
“To all the Blues, to my teammates, to all my coaches, to the whole club, a huge thank you for these special moments,” Giroud tweeted.
“I am 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’s contract left at Stamford Bridge.
He started just eight Premier League games for Chelsea last season after the arrival of German strikers Kai Havertz and Timo Werner.
He was part of the French Euro 2020 campaign where the world champions were eliminated by Switzerland in the round of 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 at Sampdoria on August 22.
(1$ US = 0.7261 free, 0.8471 euro)
(Reporting by Shrivathsa Sridhar and Hritika Sharma in Bangalore; editing by Kim Coghill and Hugh Lawson)