Alonso was appointed Manager on Sunday, returning to the Santiago Bernabeu where he spent six seasons as a player and won several trophies.
The 43-year-old had been in charge of Bayer Leverkusen, who he guided to a double last season as they won the German Cup and lifted their first Bundesliga title without losing a game.
"Without a doubt, this is a very special day for me. A day that I will have marked in my calendar for life. I am very happy to be here, in what I feel is my home," said Alonso, who will begin his tenure on June 1 ahead of the Club World Cup.
"The bond with Madrid has never ceased to exist and, since I entered Valdebebas (training centre) an hour and a half ago, that feeling has been reborn. I have the feeling that this is the beginning of a new era.
"We have a great team, we have fantastic players and a very good potential. That gives me reason to come here with a lot of energy and enthusiasm. We have the conviction that we can achieve important things, worthy of Real Madrid and these European Cups."
--Reuters--