The veteran is off contract at Milan in June, so he is free to agree Bosman terms with any foreign team.
Transfer expert Fabrizio Romano is reporting Giroud has now signed a deal with LAFC. The contract will run for 12 months.
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Giroud can be considered a new LAFC player," Romano reported.
Giroud has 15 goals and nine assists in 42 appearances across all competitions this season.