The Italian side confirmed the sale of Kaka to Real in an expected world-record transfer late last night, before Madrid also announced the move on their own website.
Reports have suggested Kaka, who was also earlier linked with Chelsea, has signed for around £59million - which, if true, would smash the world record fee of £46.7m paid by Real to Juventus for Zinedine Zidane in 2001.
He had the opportunity to join Manchester City in January this year in a deal reported to be worth £100m, but opted to stay in Italy.
At a press conference in Recife, where the player is currently on international duty ahead of Brazil's World Cup qualifier against Paraguay later today, Kaka revealed he rejected the move to England as he did not want to leave Milan mid-season.
"I can officially say I'm a Real Madrid player. My professional link with AC Milan finishes now, but my sentimental link will never end," he said.
"Real Madrid intend to build a great team, with historic players such as Raul and Casillas. We will make history again, both in Spain and Europe. I guess the sport project is very good.
"Manchester City and Real Madrid are two different clubs with different situations. At that time (January), it was mid-season, I had a strong emotional impact due to the Italian fans requesting me to stay, and I decided to stay.
"Now another chance came up and AC Milan is in a big crisis (financially). For me, the sporting project (at Madrid) is interesting and will be an important boost to continue my career in the highest level."
"I wanted to stay on at Milan, but the world (financial) crisis affected a lot of clubs, especially those like Milan which are businesses," he continued.
"So then, I spoke with the Milan directors and we reached the conclusion that the best thing for everybody would be to sell."
Kaka also revealed that new Real president Florentino Perez has been busy "making contact" with potential targets as he looks to revive his 'Galacticos' project.
In Perez's previous stint with the club, he oversaw the acquisitions of global stars of Luis Figo, Ronaldo and David Beckham, as well as Zidane.
The likes of Cristiano Ronaldo, Xabi Alonso, David Villa and Franck Ribery have also been linked to the Spanish capital club since Perez's unopposed election signalled the return of their vast spending.
"The president (Perez) is already making contact (with potential signings) and is putting together a competitive team, one which will try to once again become champions in Spain and Europe. That's why I chose Madrid.
"They have historic players there already, such as Raul or (Iker) Casillas. Real Madrid will be an important challenge for me. We're going to win many titles again."
Kaka also admitted he had received plenty of advice on the move from former Real player and Perez signing Beckham, who spent a short spell at Milan on loan earlier this year.
He also revealed that although the deal was only announced last night, it had been in the pipeline for some time.
"I spoke to some friends, like Beckham, who has already played for Real. He said it's a fantastic place to play. I spoke to him this past week and he kept helping me, he said I made a positive choice for my career's growth," Kaka revealed.
"I wanted this move to be announced sooner. For me it's a relief that it has been announced now, although I have always be 100% focussed on the national side.
"I've been weighing up the offer from Real Madrid a lot. It's an important project for me to continue growing in my career. I'm not going to Real Madrid for money, as I had other offers. But I knew I would only leave Milan to play for Real Madrid.
"Only small details were missing, such as the medical exams I passed this morning. The deal was sealed long time ago".
He also said he hoped to put an end to Barcelona's dominance of Spanish and European football, after the Merengues' arch-rivals swept all before them this season en route to claiming Spain's first league, cup and Champions League treble.
"This will be a tough season at Real Madrid, after all that Messi conquered with Barcelona," he said.
"They're the big favourites and deservedly so. I hope Barcelona's hegemony will end in the coming years. Real Madrid will build a great team to win titles again, as it's the club's history"
Meanwhile he revealed he fell uncomfortable taking on the number five jersey once worn by Zinedine Zidane.
Perez had admitted he would like to see the Brazilian playmaker take on the shirt, but Kaka said he would not feel comfortable doing so.
He said: "Wearing the number five would be a great responsibility. Zidane was a great player, both for Real Madrid and for France, and I wouldn't like to wear the same number as he did.
"We're going to wait a bit before deciding which one to use."
And finally he had words of gratitude to Milan for launching his career in Europe, while he was also elusive about whether he would end his career in Madrid.
"I will be 33 years old by the time the (Madrid) contract ends, with the World Cup in Brazil in 2014 still to come. Lots of things will happen," he said.
"I'm not thinking today in ending my career at 33. I expect to write history there and sign a new contract, who knows, until 35. May be I'll retire then."
He added: "I want to thank Milan, as they were the club who put me on the international scene. They gave me the opportunity to become a big name in Europe.
"I'm happy to leave Milan by the front door, with a lot of friends. It has been very emotional to see what the Milan fans have done for me."
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