The former France midfielder will leave the Stade Gerland at the end of his contract after three years in charge
The 48-year-old has been in charge since 2011 but has opted to take a break from the game for personal reasons.
He said at a press conference on Tuesday: "I will no longer be an employee of the club on July 1. This is a break I need for family and personal reasons.
"I need to take a break and breathe.
"I will not be on another bench next season.
"I would like to thank the players, coaching staff and supporters without whom the club would be nothing."
Garde, who played for Lyon, Strasbourg and Arsenal in his playing career, succeeded Claude Puel as Les Gones' boss in 2011 and led the club to the Coupe de France trophy in his first season in charge.
League placings have also been respectable. Lyon finished fourth in 2012, third in 2013 and are currently fifth heading into the final weekend of the Ligue 1 season.
Having failed in his attempts to persuade Garde to stay, club president Jean-Michel Aulas must now find a successor and he says he is clear on the kind of person he wants.
He said: "We have defined a profile, it is directly related to the business plan of OL. That is to invest in training and infrastructure.
"We will not employ a coach who does not speak French or will want to come with a bloated staff.
"We will take into account the possibility of integrating the existing staff."