Tigers were awaiting official clearance from the French Rugby Federation and the 30-year-old, who has won 35 Test caps, is now able to cover for injured duo Manu Tuilagi and Matt Toomua.
Head coach Aaron Mauger said: "We are missing two big players in midfield.
"We're very happy to be able to bring in a player of Maxime's style, quality and experience."
Leicester have completed the signing of France centre Maxime Mermoz from Toulon until the end of the season.