According to Sky Sport Italia, the France international will fly in for his tests at the start of next week and put pen to paper.
He had agreed personal terms months ago for €3.5m per season, with an expiry date of June 2023.
The only issue was finding an agreement with Chelsea, who activated their unilateral option to extend his contract, whereas the Rossoneri were convinced they’d be able to sign him as a free agent.
Multiple sources in Italy today claim the deal has been struck, with Chelsea accepting €1m plus another €1m in rather difficult to complete performance-related bonuses.
Giroud will play in Serie A and the Champions League for Milan, who had already attempted to sign him last season.
The centre-forward turns 35 at the end of September.
AC Milan have reached an agreement with Chelsea to sign Olivier Giroud, here-we-go soon! €1m as guaranteed fee, €1m as add on. Giroud will sign until June 2023 once all details will be fixed. 🇫🇷 #ACMilan
— Fabrizio Romano (@FabrizioRomano) July 8, 2021