Despite seeing a new 12 month option triggered by Chelsea last month, Giroud is ready to move to Milan after France's Euros campaign.
Gazzetta dello Sport says the centre-forward has agreed a two-year deal with Milan, with the option for a further 12 months. The agreement is worth €4m-a-season.
Giroud is now waiting on Chelsea to make their stand clear.
There is hope inside Giroud's camp that Chelsea will agree to release him on a free transfer to smooth the switch to Lombardy.