The new los Blancos signing hopes his Spain Under-21 team-mates will help him settle in at the Santiago Bernabeu and has pledged to give his all for his new side
The midfielder was showcased to fans on Saturday following his €32 million [£27.6m] move from Real Sociedad on a six-year deal and it has not taken long for him to shower praise on the Ballon d'Or-winning Portuguese winger.
"Madrid have amazing footballers, but I think Ronaldo is the star attraction," he told the club's official website.
"He’s incredible, the best in the world and we need to go all out with him. Let’s hope we have a great year, full of successes."
Illarramendi has pledged to give 100 per cent in a Blancos shirt and hopes that the presence of Spain Under-21 team-mates in Carlo Ancelotti's side will help him settle in with ease this summer.
"I think I’m someone who gives my all every day and who tries to get better every day," the 23-year-old added. "On the pitch I also try my heart out.
"How things turn out well depends on many factors, but it won’t ever be for lack of effort. When I go out to play I try to do my best, with the best possible attitude.
"I know some players from the national team already and that will help me adjust. They are good friends and I think between us all the team will be great."