* Second biggest transfer fee ever
* Presentation expected at end of June
Reports said the transfer fee was around 68 million Euro (about £58.6m), which would make it the second biggest ever after Zinedine Zidane joined Real from Juventus for around 73m Euro in 2001.
"Everything I've always done for Milan has been by mutual agreement, from the moment I arrived until my departure today," he told a news conference at the Brazil team hotel. "I'm leaving by the front door."
"I've won everything that I wanted as a player and this is a new motivation for me."
"I'm sure Real Madrid will build a competitive team which can start winning titles again."
"We are working on building a good team, an important team, and this has only just begun," Perez told radio station Onda Cero.
"AC Milan thanks the man Kaka and the champion Kaka for his decisive contributions to so many victories obtained in the last six years," the Serie A club said in a statement.
"His loss on the field, though serious, can be filled. It will, however, be very difficult to fill the void left by Kaka the man."
Perez has promised to deliver a "spectacular sporting project" built around the world's greatest players, and local media have spoken of a 300m-Euro war chest which will be used to finance a second 'Galactico era' at the Bernabeu.
Having lured the likes of Luis Figo, Zinedine Zidane and David Beckham to Madrid earlier in the decade, Perez's flagship first signing on his return was Kaka, a move seen as both a declaration of intent and a dig at his predecessor.
He has also spoken of interest in Manchester United's Cristiano Ronaldo, Bayern Munich's Franck Ribery, Liverpool's Xabi Alonso and Valencia duo David Villa and David Silva.
