The Croatia international has been at the centre of a tussle between Spurs and the Spanish giants throughout the summer but managed to finalise a five-year contract at the Bernabeu today.
"Everything started before the Euros," said Modric. "It was hard as I wanted to be [at Madrid] as soon as possible, but sometimes negotiations go on longer than expected.
"Now I am very happy to be here. Of course it has been a tough time, almost one month without training fully with a team, but finally it has been done.
"I want to thank all the people at Tottenham. I had four great years there, and I enjoyed every moment. I want to thank everyone who made my life enjoyable in London. There are no hard feelings on my side, this is a new page in my life. I am looking forward."
Reports have claimed that the deal is worth up to £33m.