Thomas Gravesen has completed his move from Everton to Real Madrid after passing his medical.
BBC Sport understands Real will pay around £2.5m for Gravesen, 28, who has signed a three-and-a-half-year deal.
"This is a dream for me," said the Dane as he was unveiled in Spain. "This is the biggest club in the world. I am very proud and pleased to be here."
And Real president Florentino Perez added: "He is without doubt the player we were missing."
"He's a fighter and has a great competitive spirit but he's also a technically gifted player. I am sure he is going to do great things this season."
The Danish midfielder joined Everton from Bundesliga side Hamburg for £2.5m in 2000 but was out of contract in the summer.
"I loved my time at Everton and would like to place on record my thanks to all the supporters, players, officials and coaching staff of the club," he said.
"Leaving was a difficult decision. But the opportunity to join Real Madrid,which is one of the world's great football clubs, comes only once in a lifetimeand was not one I could decline.
"I genuinely wish Everton every success for the remainder of the season."
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.
Moyes told the Everton website: "We didn't want to lose him. We had a right to turn around and say, 'You're not going'.
"But we've taken 3.5m euros, plus a 20% sell-on fee and a buy-back clause for him - plus one or two odds and ends to go on top of that deal.
"So with six months of his contract to go, with a player who wants to leave, it was the best deal we could get out of the situation."