The 22-year-old has been in fine form for the French Ligue 2 side, netting six goals in 20 games, and Foxes manager Nigel Pearson could not hide his delight at securing his services.
Pearson said: "Riyad is a pleasing addition to a squad that already has a lot of quality and I'm delighted we've been able to secure his signature.
"Whenever we look to add to our squad, it has to be a player that will improve us while complementing what we already have and Riyad certainly fits that description.
"He is a talented player, technically very good, and he gives us another option in attacking positions."
The deal is waiting for Football League approval and international clearance but should the paperwork be finalised, Mahrez will be available to make his debut when the Sky Bet Championship leaders travel to Leeds next Saturday.