The 22-year-old Frenchman has signed a 5-year-deal and will join up with his new Foxes teammates for the start of pre-season later this month.
Gianluigi Donnarumma will leave AC Milan next month as his contract expires on June 30, the 22-year-old goalkeeper made 251 appearances for the Italian giants.
Lille manager Christophe Galtier, who led them to their first Ligue 1 title in a decade, on Sunday announced that he will leave the club.
The French Ligue 1 capped an epic season this time around with an unlikely title winner, with LOSC Lille being crowned champions.
With 77 points in the league before the last trip to Lens, Kovac and his men have largely exceeded the objectives set at the season's start.
Paris Saint-Germain's record away from home in Ligue 1 this season is largely positive.
Top three teams Lille, PSG and Monaco can with the Ligue 1 title as they are separated by just three points going into the final match day
Leaders Lille ease past 10-man Nice, while PSG remain hot on their heels with only three round of matches to play in Ligue 1.