Real confirmed that they have reached an agreement with HSV and that Van der Vaart is set to sign a five-year deal.
The 25-year-old will be presented by the Madridistas on Tuesday.
Earlier on Monday, Van der Vaart said in an official statement carried by his website that he is joining the Spanish giants.
"I'm going to play for Real Madrid it's a dream come true," said Van der Vaart, who used to be Hamburg captain.
"I have always wanted to move to Spain because I have a strong bond with that country."
Van der Vaart, whose mother is Spanish, was poised to complete a move to Valencia last season but his German club refused to let him go.
He is believed to be the replacement for Cristiano Ronaldo, after Manchester United refused to sell him.
Van der Vaart's move out might give Egypt forward Mohamed Zidan a chance to feature regularly for Hamburg next season.