Madrid finished the 2020/21 campaign in second place, two points behind city rivals Atletico.
They went out in the early rounds of the Copa del Rey and lost to Chelsea in the semi-finals of the Champions League to register their first trophyless season since 2010.
"It is now time to respect his decision and show our appreciation for his professionalism, dedication and passion all these years," Real Madrid said in a statement on its website.
Legend
"Zidane is one of Real Madrid's great myths and his legend beyond his role as coach and player at our club."
Zidane, who played for Madrid between 2001 and 2006, took over as head coach in January 2016 following the dismissal of Rafael Benitez.
That year the former France international led them to the Champions League crown, the European Super Cup as well as the Club World Cup.
In 2017, after securing the La Liga crown, his side became the first team to win back to back titles since the Champions League format emerged from the European Cup in 1992.
A Spanish Super Cup as well as another European Super Cup and Club World Cup were added to the haul.
A year later, Zidane became the first coach to guide a side to three consecutive Champions League crowns. Shortly after the triumph, he quit.
Return
With Madrid struggling under the disastrous spell of Santiago Solari, Zidane returned in March 2019 and added the 2020 La Liga title and Spanish Super Cup to their collection.
“I learned a lot from him,” said Madrid defender Raphael Varane. "He has been a source of inspiration for me and for many players. I wish him all the best for the future. He is a great coach."
