The two sides did not reveal the transfer fee but both Danish and French media reported that Lille had paid Copenhagen 17 million euros for Haraldsson.
"The battle was hard and long but with Hakon's decisive support and determination, it is now done," Lille President Olivier Letang told the club website.
"He is a player who was the subject of many requests in Europe and his profile allows him to play in different attacking positions. We will now be able to integrate him into the LOSC family so that he adapts to France and Ligue 1."
Haraldsson joined Copenhagen as a 16-year-old from Icelandic side IA Akranes in 2019 and has made nearly 60 appearances in all competitions, including six in the Champions League, since his first-team debut in 2021.
He helped Copenhagen to win two Danish Superliga titles in the two recent campaigns, also winning the Danish Cup in 2022-23.
"Hakon has gone from a young talent to a top player and therefore it is logical that the interest in him has been great," said Copenhagen sporting director Peter Christiansen.
Haraldsson, whose parents are former national team players, made his Iceland debut in June 2022 in a friendly 2-2 draw against Israel. Since then he has earned 10 more caps and scored one goal.
