Hollande said in a statement that the prize recognises "a considerable body of work which explores the subtleties of memory and the complexity of identity".
Modiano, 69, described by one critic as "1 metre 90 of shyness and candour," is one of France's most celebrated writers, and a winner of the country's top literary award the Goncourt.
Modiano said was "very happy" at his victory, but "with his customary modesty told me that 'it's weird'," his editor Antoine Gallimard told AFP.
France's Culture Minister Fleur Pellerin also praised the victory, a rare boost for a nation rendered morose by months of bad economic news and a gloomy political scene.
"This is a happy day for French literature," said Pellerin, saying she felt "very emotional and extremely proud for France and all our fellow citizens."
She said Modiano "represents the influence and vitality of French literature in the eyes of the world.