Zidane announced his departure at a news conference on Thursday, just five days after leading Madrid to a third Champions League title in his third season in charge.
'This is a lovely moment as we have just won a third straight Champions League and I have now reflected and made this decision.
Gareth Bale, who scored twice in Real's 3-1 win over Liverpool in Saturday' Champions League final, and Cristiano Ronaldo have both cast doubts on their future at the Bernabeu since lifting the trophy.
Zidane, speaking at the press conference, said: 'I'm not going to coach another team right now. "I had to do this for everyone". Zidane drew criticism all year - as any Real Madrid manager would, no matter how successful he is.
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Manchester United's first choice right-back is of course Antonio Valencia , but at 32, he is edging towards the end of his career. United have moved quickly amid interest in Dalot from clubs including Juventus, Napoli, Real Madrid and Barcelona.
Ryan Gaydos is an editor for Fox News. I love this club, I love the president, he's given me the chance to come as a player and a manager.
Ramos' Madrid team-mates also paid tribute on social media to Zidane with many calling it a pleasure to have been coached by their idol.
"After three years, it's my decision and perhaps I can get it wrong, but I think that after such time it is the moment".
When pressed on whether or not the various crises surrounding Real Madrid and their star players had forced him into this decision, the Frenchman was quick to quash such speculation. I thank you all for your support and there are hard times when there are whistles but that is part of this club.
" 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. For me and for everyone, today, a change is needed and that is why I have reached this decision".
"It's my decision", he said.