Varane had been a transfer target for Manchester United, as well as domestic clubs Paris Saint-Germain and Lille.
Despite previously suggesting that the 18-year-old would not be transferred abroad, Lens president Gervais Martel has disclosed that the Bernabeu is the chosen destination.
"He is going to play for Real Madrid under the guidance of Jose Mourinho who he has already met, just as he has Real advisor Zinedine Zidane,” France Football quotes him as saying.
"Raphael is an exceptional boy. I am proud that he is going to don the Real colours. He was invited to Real two months ago and visited the facilities. He told me: 'I cannot turn down such an opportunity!'
“I am sure he will naturally make his place there.”
Varane made 23 appearances for Lens last season, which ended in relegation to Ligue 2.