The Spanish midfielder has joined Real from Getafe for an undisclosed fee and has penned a six-year contract with the Spanish giants.
"Thanks to Real Madrid I can fulfil a dream that I had as a child," said Leon. "I will give everything for this jersey and I hope I can win many titles."
Real president Florentino Perez handed Leon his jersey in a low-key presentation at the Bernabeu.
"We said we wanted great Spanish players and Leon has the quality, the capacity and the personality to wear the Real Madrid colours," said Perez.
"We hope he will lift many trophies and in the future be selected for the national team."