Navas, one of the stand-out goalkeepers in this summer's World Cup, moved from Levante on Sunday for a reported fee of 10million euros (£7.9m).
But with Diego Lopez and Iker Casillas already at the Santiago Bernabeu, the 27-year-old is not expecting an easy ride.
"Becoming the starter is complicated, I will work at Real Madrid with humility," he told AS.
"God does not put things before you that you cannot overcome.
"A six-year contract gives me peace of mind. I'll learn a lot from all the players. It's a great opportunity that I want to make the most of."