Alain Perrin has been appointed Lyon coach.
Former Portsmouth and Marseille coach Perrin, 50, steered Sochaux to French Cup success this season. He replaces Gerard Houllier, who resigned last week after two years in charge.
Perrin had already revealed he had accepted an offer from Lyon but talks over financial compensation for Sochaux president Jean-Claude Plessis, had delayed the deal.
A deal was reached late on Tuesday with Lyon reportedly agreeing to pay Sochaux around 500,000 euros.
Former France and Liverpool manager Houllier, 59, confirmed on Friday he was leaving Lyon after leading them to two consecutive Ligue 1 titles.
Sochaux chairman Jean-Claude Plessis has reportedly already lined up Le Mans boss Frederic Hantz as Perrin’s successor.
However, Le Mans chairman Henri Legarda has not yet given up hope that he will stay at the club.
“I would like him to stay,” he told the French press. “On Tuesday, I spent three hours trying to convince him.
“He has a contract and I would like him to respect it. I believe (the chances of him staying are) 50-50.”