The Costa Rica international, who starred at this summer's World Cup in Brazil, says he will fight tooth and nail for a starting berth - just as he did at former club Levante
The 27-year-old goalkeeper earned a summer switch to the Santiago Bernabeu on the back of a stellar season at Levante and a string of sensational displays for Costa Rica at Brazil 2014.
His arrival in the Spanish capital has already prompted the sale of Diego Alves to AC Milan and Navas is now set to challenge Casillas for a starting berth in Carlo Ancelotti's first-choice 11.
He insists that he does not want to develop a rivalry with the Blancos skipper but is nonetheless determined to fight for his place, just as he did at his former club.
"I had difficult moments with [former Levante goalkeeper Gustavo] Munua and I tried every day to improve and decided to never give up and I trained as though I would start every game," Navas told reporters on Wednesday.
"I have always faced everybody in a responsible way and I will do what I have always done.
"I will try to learn from Iker and I have to give one hundred per cent.
"I can talk about what I have experienced so far and for me it has been worth it being at Madrid and nobody knows what will happen in the future.
"Right now I am here to enjoy the Levante fans and we'll see what the future brings. Only [Ancelotti] knows who the goalkeeper will be.
"I know what I have to do and I'm not thinking about anything else. I know what I am capable of and that is to train hard. I am relaxed and content. I want to repay the confidence Real Madrid have shown in me because they have made me feel very welcome."