Zidane revealed his decision in a hastily-arranged press conference in the Spanish capital on Thursday. President Florentino Perez appeared alongside him and revealed it was an "unexpected decision".
"I have taken the decision not to continue next year," Zidane told the media.
This is the right moment for everyone, it might seem a bit strange, but it had to be done for the good of everyone, the players, the club, and myself. This team must keep winning, and it needs a change after three years, another voice, another method of working.
The Frenchman also lead Madrid to back-to-back European Super Cups and Club World Cups in 2016 and 2017.
Real Madrid's assistant coaches Jose Carlos Parrales, Javir Mallo, LLuis Lopies Real Madrid's French coach Zinedine Zidane, assistant coach David Bettoni and Antonio Pintus celebrate at Cibeles square in Madrid on May 27, 2018 after Real Madrid won their
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Perez said: "This was a totally unexpected decision and today is a sad day for me and for everyone who works for this club.
When he says he's taken a decision though, we have to accept it. I tried to convince him but I know how it is. He knows he has all our love and support. One can't be prepared for something like this. I remember the first time I went to his house and asked him to coach Real Madrid and he was absolutely convinced he could win things.
"We must thank him for his care and passion for Real Madrid over these years. "The only thing I want to say is 'hasta pronto' because I know he will return, maybe after a rest."
Zidane said his association with Madrid may not be at an end. During his five-year playing career at Madrid between 2001 and 2006, Zidane won the Champions League in 2002 and La Liga in 2003. As assistant to Carlo Ancelotti, he was on the bench in Lisbon when Madrid secured La Decima in 2014.
"Like I told the president it could be a 'see you soon' because Madrid has given me everything," Zidane added.
I will still be close to the club but this decision is a clear one that might not make sense to some people but it is the moment to make a change, for the players as well. After doing three years, it's the right decision. I understand, and what I can do is thank the fans not only as a coach but as a player they have always supported me.
As to his future plans, Zidane said he was not looking to rush back into management.
I'm not going to coach another team right now. I'm not looking for another team. What's coming now, I don't have to talk about it.