Genesio, who's been criticized by a large contingent of supporters, said the "negative climate" has made it impossible for him to continue.
"It was in the best interests of the club that I took, in agreement with my president, this decision," the 52-year-old added.
Former Manchester United manager Jose Mourinho has been linked with Lyon in recent weeks.
A native of Lyon, Genesio played as a midfielder for Les Gones from 1985-1995. He's served as coach for the past four seasons, securing memorable victories over Paris Saint-Germain and Manchester City.
Despite his close ties to Lyon, Genesio has faced overwhelming hostility from fans as supporters have displayed banners and sung chants against the manager.
ESPN FC correspondent Julien Laurens reported earlier this month that Lyon president Jean-Michel Aulas - one of Genesio's strongest allies - wanted to give the coach a two-year contract extension.
But the club's recent struggles, including elimination from the Coupe de France, made Genesio's position untenable.
"I want to tell the fans that they should come cheer on their team if they want to have Champions League games next year," he said. "We need them."
Lyon, currently third in the Ligue 1 table, have never finished lower than fourth under Genesio.