Kaka is the latest big name to join Real Madrid.
According to reports in the Spanish and Italian media the Brazilian has agreed to join the Santiago Bernabeu club in a $93 million deal and an official announcement to this effect is expected soon.
It may be noted here that Kaka's coach at AC Milan, Carlo Ancelotti, has now taken up the managerial responsibility at Stamford Bridge.
Earlier, in April, a Spanish daily had reported Florentino Perez, then a favourite to win the elections for Real presidency, had reached an agreement with Milan to sign Kaka for about 60 million euros.
But the supposed deal never materialised.
The 27-year-old, under contract with Milan through 2013, was the subject of intense speculation after a bid by big-spending Manchester City.
The 2007 world player of the year almost joined City in January for a world record fee in excess of 100 million euros ($142 million).
On Tuesday, AC Milan owner Silvio Berlusconi admitted the club will find it difficult to hang on to Kaka.
"I don't know if we will be able to keep Kaka at Milan because they offer him so much money," he was quoted as saying.
Kaka, who is away with the Brazil squad, had earlier told reporters he did not want to leave Milan.
"To the millions of Rossoneri fans I say my decision has been made," he said. "I have said I want to stay. Now please leave me in peace."
But perhaps this was an offer he couldn't quite resist.
The 27-year-old made 31 appearances in Serie A this season for the Rossoneri, finding the back of the net 16 times in the process but failed to help them win any silverware.