If it is 65million euros it would be the second biggest ever transfer - after that of French great Zinedine Zidane, who cost Real Madrid 75million euros in 2001.
"I wanted to stay (at Milan) but the world crisis affected my decision. I knew I´d only leave Milan to play for Real," the player said at a press conference in the Brazilian city of Recife.
"I will be part of a new Real Madrid that will once again be champions in Europe and in Spain," said Kaka.
"It will be a new challenge for me and to live up to all the expectations placed on me will be motivation enough.
"I want to help write a new page in the history of the club by winning trophies with them."
Kaka had earlier undergone in Brazil a problem-free medical attended by Real Madrid´s Dr Juan Carlos Hernandez as well as the Brazilian squad´s doctor, Jose Luiz Ronco.
Real chairman Florentino Perez has established a 200 million euro war chest for players, vowing to create a "spectacular team" capable of overtaking arch-rivals Barcelona - who won the title, Champions League and Spanish Cup in coach Pep Guardiola´s first season in charge - next season.
Perez oversaw the era of the "Galacticos" when he was in charge at Real between 2000 and 2006, when world stars such as Zidane, England´s David Beckham and Brazil´s Ronaldo were attracted to the club.
Kaka has been at AC Milan since arriving from Sao Paolo in 2003, scoring 70 goals in Serie A and 23 in the Champions League.
He has won the 2007 Champions League with them, the 2004 league title, two European Super Cups and the world club championship in 2007.
He had been the subject of a massive transfer offer from English Premier League side Manchester City in January but the deal eventually came to nothing.
Kaka, who was in Brazil on World Cup duty for his country, said that although a new page in his career was opening up he would always have a soft spot for AC Milan despite their decision to sell him.
A statement from AC Milan read: "It will be very difficult to fill the void that will be left by Kaka.
"We offer him the most cordial and affectionate wishes for the continuation of his sporting career.
"He is a shining example of professionalism and commitment.
"AC Milan thank the man and the great champion Kaka for his decisive contribution to the many victories achieved in the six years of his commitment."
Kaka´s official unveiling in Madrid is unlikely to take place until the end of the month because after Wednesday´s World Cup qualifier against Paraguay in Recife he will travel with the squad to South Africa for teh Confederations Cip which starts next Sunday.
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