Madrid gave no financial details but reports late said the Spanish club will pay Milan €65 million ($NZ145 million) for the attacking midfielder, making it the richest deal in football history.
The largest previous transfer was set by Zinedine Zidane when he joined Madrid from Juventus for US$65 million in 2001.
Milan also confirmed Kaka's transfer to Madrid on its website.
Kaka, who passed a medical in the northeastern Brazilian city of Recife earlier Monday, has signed a six-year contract.
"Kaka is one of the players that every team would like to have and Madrid had the chance to get him," Madrid president Florentino Perez told radio station Onda Cero just before the signing was announced.
The attacking midfielder is the first player to join Madrid since Perez regained the club presidency unopposed last week.
Perez has said he intends to revive his "galactico" policy which, as well as Zidane, attracted star players like David Beckham, Ronaldo and Luis Figo to Madrid earlier in the decade.
Kaka, who was the 2007 FIFA world player of the year, earlier this year turned down a world-record €100 million transfer to Manchester City last season.
Kaka, who is in Brazil with the national team for World Cup qualifiers and who will then travel to South Africa for the Confederations Cup, said before he left he was happy in Milan.
However, the size of Madrid's bid appears to have proved too good for Milan to turn down. Last week, Milan president Silvio Berlusconi and chairman Adriano Galliani said the club had made huge financial losses recently.
Madrid's interest in signing Kaka goes back some years. Former Madrid president Ramon Calderon pledged he would sign the player in 2006 when he was running for election.
Perez told Onda Cero that Madrid's pursuit of the 27-year-old Brazilian, whose real name is Ricardo Ezecson Dos Santos Leite, was aided by a collaboration agreement it has with Milan. Milan vice president Adriano Galliani was reportedly in the Spanish capital last Tuesday to pave the way for the deal, along with Kaka's father/manager Bosco Leite.
Perez is expected to attempt to sign several more top names for Madrid before the start of next season. Last week, he announced that Madrid would also be looking to land Manchester United's Cristiano Ronaldo.
Perez is hoping to revive Madrid's fortunes after a poor season in which it failed to win any silverware while arch-rival Barcelona won the Champions League and the league and cup double. Nine-time European champion Madrid has not reached the quarterfinals of Europe's top club competition in the past five seasons.
Last week, Madrid appointed Chilean Manuel Pellegrini, formerly of Villarreal, to replace Juande Ramos as coach.
The departure of Kaka, who won the Champions League with Milan in 2007 and the Italian league in 2004, came a week after the Italian club's coach Carlo Ancelotti left to take charge of Chelsea.
Kaka factbox
Born: April 22, 1982 in Brasilia, Brazil
EARLY CAREER
* Makes an immediate impact for Sao Paulo scoring 12 goals in 27 appearances in the 2001 season.
* Plays just 18 minutes in the 2002 World Cup which Brazil win.
ITALIAN MOVE
* Moves to AC Milan in 2003 and makes his debut on Sept. 1 in a 2-0 win over Ancona. He goes on to score 10 league goals and four Champions League goals in his first season and then spurs Milan to the Italian title in 2004.
* Helps Brazil to the quarterfinals of the World Cup in 2006.
* Real Madrid make their interest well-known following the tournament and Kaka firmly establishes himself as one of the best in the world as he inspires Milan to their seventh European Cup title in 2007.
* Wins FIFA World Player of the Year award and the Ballon d'Or in 2007.
* A nagging knee injury hampers his 2007/08 season at Milan, who finish a disappointing fifth in Serie A and lose to Arsenal in the Champions League first knockout round.
* Manchester City bid a world-record fee of more than 100 million euros ($142 million) for him in Jan. 2009 but talks fall through. Milan end the season third in Serie A.
REAL TRANSFER
* Kaka expresses his love for Milan but following coach Carlo Ancelotti's departure for Chelsea and Florentino Perez's re-election as Real president, a deal worth a reported 68 million euros is done quickly with the Serie A side in need of funds to reinvest.
