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 city rivals Arsenal in 2018.
“To all the Blues, to my teammate s, 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.”
The 34-year-old started only eight Premier League games for Chelsea last season under manager Thomas Tuchel 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.
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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.
The Rossoneri, who finished second in Serie A last season behind city rivals Inter, begin their 2021-22 league campaign away to Sampdoria on August 22.