Modric completed a medical at the Spanish giants earlier today after the two clubs had agreed a fee for the player this morning.
The 26-year-old's move has been one of the longest transfer sagas of the summer due to disputes over finances, with the two clubs eventually settling on a price believed to be at least £33m.
The Croatia international made no secret of his desire to join Madrid, and was quick to declare his excitement at signing for the "biggest" team in the world.
"I'm very happy, honoured and proud to be at the biggest and best club in the world. I'm very excited," said the midfielder.
Modric scored 17 goals in 160 games for Spurs during his four years at the club, and was voted their player of the year during the 2010-11 season.