Mahrez had been heavily linked this week and has finally completed his move to the King Power stadium subject to international clearance.
The 22-year-old has joined Leicester on a three-and-a-half year contract though the fee paid to Le Havre has not been disclosed.
The French-Algerian has been in a rich vein of form for Le Havre where he has six goals and five assists in 20 matches for the Ligue 2 side this season.
Leicester manager Nigel Pearson said he was delighted with the acquisition of Mahrez insisting the winger will give his side another dimension in the final third of the field.
"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," Pearson told the club's official website.
"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."
Mahrez could be in line to make his debut for his new club in next weekend's visit to Leeds United in the Sky Bet Championship.
Leicester extended their lead at the top of the table with a 4-1 win over local rivals Derby County on Friday.
Another Leicester target is Crystal Palace striker Kevin Phillips whose contract at Selhurst Park expires this weekend.
On Friday, Pearson admitted Phillips would be a very welcome addition to his squad.
"There's no such news (on Phillips) but we are certainly very interested in him."