Giroud, 34, is set to undergo a medical with Milan on Friday morning before completing the formalities of the move, believed to be worth 3m pounds.
The veteran striker has been with the European champions since 2018, having joined from Arsenal.
He has never played in Italy, with his entire previous professional career spent in his native France, with a prolific spell with Montpellier.
Chelsea are understood to be keen to spend this off-season, with owner Roman Abramovich desperate to win the Premier League for the first time since 2017.
Abramovich was reportedly delighted with Thomas Tuchel’s impact after arriving as manager midway through the campaign, leading the side to a top four finish and winning the UEFA Champions League.
The Blues are in the hunt to sign Borussia Dortmund forward Erling Haaland for a significant fee.
World Cup winner Giroud is expected to join Milan on a two-year contract.
He has scored 39 goals in 119 appearances for Chelsea, winning two FA Cups, the Europa League and last season’s Champions League.