Le Bris moves from Lorient and has signed a three-year contract with the Black Cats.
He spent two seasons in charge of Lorient, guiding them to 10th in Ligue 1 in his first campaign before they finished 17th and were relegated last season.
Le Bris takes charge at Sunderland after Michael Beale's sacking in February.
"I'm certainly here to pass on my energy and my convictions, but also to listen and learn," Le Bris told the club's website.
"I want us to bring joy to our fans, not only through results, but also through our style of play, and I'm convinced that with commitment and hard work, we can write an exciting new chapter."
Sporting director Kristjaan Speakman said: "Le Bris is a talented coach, who is thoughtful and detailed in his approach and values strong relationships with players and staff".
"He is aligned with delivering our playing identity and he shares our ambition to win, as well as our passion for talent development."