Real Madrid's new player Asier Illarramendi (L) poses with Real Madrid's president Florentino Perez during his official presentation at the Santiago Bernabeu stadium in Madrid on July 13, 2013. (AFP/Dani Pozo)
Club president Florentino Perez hailed the 23-year-old Basque as "one of the brightest hopes of Spanish football", following his role in Spain's victory in the European under-21 championships.
"You will be playing in front of a home crowd that is demanding but unique. These supporters will give their all and they will demand that you do too," Perez told the former Real Sociedad midfielder.
Real Madrid surprised "Illarra" by headhunting him from his boyhood team earlier this month.
"A few days ago I would never have dreamt that I would wear a different shirt from that of Real Sociedad," he said on Saturday.
"This is a unique opportunity for me. I will give everything I have for these colours."
Beaten in the league by Barcelona and knocked out of the Champions League at the semi-final stage last season, Madrid are looking to improve under new Italian coach Carlo Ancelotti.
Illara will play in midfield alongside another new signing, Spain international Isco, who joined from Malaga.
"The Basque footballer brings youth, impact on the game, touch and judgement to Real Madrid", the club said in a statement.