“I will be playing my final two matches with Milan and will continue my career in the MLS,” Giroud said in a TV interview.
“I’m very proud of what I’ve achieved at Milan in the last three years. My time with Milan might be finishing this year but the club will remain in my heart.”
LAFC is expected to formally announce the signing later this week.
The 37-year-old striker, who helped France to a World Cup title in 2018, was photographed Monday wearing an LAFC scarf, with a team jersey and cap on the table in front of him. Giroud, whose MLS contract reportedly runs through 2025, will be reunited with former French captain Hugo Lloris at LAFC.
Before joining Milan in 2021 and leading the team to a league title, Giroud won Champions League, Europa League and FA Cup titles with Chelsea. He also won three FA Cups in six years at Arsenal.
His 57 goals in 131 matches for France is six more than second-highest scorer Thierry Henry.
On Monday, LAFC also announced it has hired Neil McGuinness as the first technical director in team history. McGuinness had previously served as director of scouting and player recruitment for the reigning MLS champion Columbus Crew.