Molby says Gravesen is Real deal
Thomas Gravesen is due to be unveiled by Real Madrid after passing his medical for his move from Everton.
BBC Sport understands Real will pay around £2.5m for Gravesen, 28, who has signed a three-and-a-half-year deal.
Agent John Sivabaek said: "Thomas is very excited, but sad because he had five fantastic years at Everton."
The midfielder was out of contract in the summer and Sivabaek added: "He was very happy at Everton, but when Real Madrid want you, you cannot say no."
Everton boss David Moyes will now move to line up a replacement for the Dane, with Spurs winger Simon Davies and Blackburn's David Thompson potential targets.
A statement from Real on www.realmadrid.com confirmed: "Real Madrid have reached an agreement for the transfer of Thomas Gravesen to the White Club (Real).
"Gravesen will play for Real Madrid in what remains of this season and three more."
Real have called a media conference for Friday evening where, it is thought, they will unveil Gravesen.
Everton chief executive Keith Wyness told his club's website: "No-one at Everton wanted to lose Thomas Gravesen. We did everything we could to keep him.
"Once it became clear that Thomas had his heart set on a move to Real Madrid, we fought hard for the best possible deal for Everton. To that end we feel we have been successful."
The Dane joined Everton from Bundesliga side Hamburg for £2.5m in 2000.
He has been outstanding this season as Everton have established themselves in the top four of the Premiership.