Zidane is confident the 18-year-old will blossom under Jose Mourinho after comparing him to former France centre-half, and current Les Bleus boss, Laurent Blanc.
Zidane said: "He is a very promising player and was an obvious target for a club such as Real Madrid seeking talent.
"He is a player I like very much and in many ways resembles Laurent Blanc. I haven't seen many players like that.
"Varane has a great future. The fact many top clubs wanted him is an indication he has talent.
"I am also happy because he is French. I know people in France would have liked him to stay here but I am just doing my job."