
Real also confirmed the deal, saying that the midfielder Sneijder, 23, will sign a five-year contract.
The agreement came after Ajax rejected an earlier Real ultimatum to sell Sneijder for no more than 24 million euros, and not the 27 million Ajax wanted after an original demand of 30 million euros.
"We are proud that another player raised in our club leaves for a European top club, following Ryan Babel (Liverpool)," said Ajax technical director Martin van Geel.
"We are saddened that he will miss the important qualifiers for the Champions League. But we couldn't deny him this opportunity."
The 35-times capped Sneijder went through the full famous Ajax youth sector and made his first-team debut aged 18 in February 2003. He scored 57 goals in 180 league matches for Ajax.
Another Dutchman, Royston Drenthe, was also expected to complete a Real move this week, from Feyenoord Rotterdam. In addition, the Spaniards are reportedly after Dutchman Arjen Robben from England's Chelsea.
Other Real Madrid hirings include defender Christoph Metzelder, striker Javier Saviola and goalkeeper Jerzy Dudek.