The defender, now 20, was 18 when he left Lens and failed to make an impact in his first season at the Santiago Bernabeu.
However, the France international believes that he is now completely integrated within the Blancos set-up having broken into the first team in 2012-13 under Jose Mourinho.
"No, I did not sign too soon," the France international told AS. "I was ready to play for Madrid.
"It took me a year to adjust, get my bearings and get used to the club in general. Last season everything went well. So from now on, it should get even better."
Varane has only made six appearances for Carlo Ancelotti's side this season due to picking up a number of injuries, though the center back says he is not letting his fitness issues get him down.
"Injuries are very common in the careers of players and you have to keep faith, be confident and above all not throw the towel in and lose hope," he added.
Real Madrid is in action against Valencia in the final Liga match of the year on Sunday, though Varane is not fit enough to return to the side.