The former Chelsea, Arsenal and AC Milan striker has agreed a two-year deal with Lille.
Giroud said today: "I want to thank all the fans, my teammates and the staff at LAFC for making this stage of my career so enjoyable.
"I am happy to have contributed to the success of LAFC. From winning a trophy last season to participating in the Club World Cup, it has been a wonderful experience in Los Angeles for me and my family."
Giroud's LAFC deal was due to expire at the end of the calendar year.
"Olivier was an exemplary professional during his time at LAFC," said in a statement co-chairman and general manager John Thorrington . "He brought humility and a winning mentality that helped elevate everyone around him. Olivier was a great ambassador for the club on and off the field.
"We are grateful for his contributions and wish him, his wife Jennifer and his family the best in this new chapter."