The Croatian moves to Spain for a fee of 33.2 million pounds after a lengthy transfer saga, signing a five-year contract at Santiago Bernabeu and being handed the No.19 shirt.
Modric arrives on a five-year deal, and will wear the No. 19 shirt at Santiago Bernabeu, as the No. 14 he wore at Spurs is already taken by Xabi Alonso.
The Croatian international played no part in the north Londoners' Premier League campaign this year as the two clubs finalized negotiations for the deal, which also includes a long-term 'footballing partnership'.
"I'm very happy," he told reporters. "It's an honor to be at the biggest club in the world. I want to start training and playing for Real Madrid. I look forward to playing with the team. This is my biggest challenge as a footballer and I am sure that I will accomplish my objectives."
Modric is hoping to get on the field as soon as possible for Real Madrid, which beat out rival Barcelona to win La Liga last season.
"My challenge is to earn a place in the team, and for that you must work hard. It's going to be difficult, but I'm ready. My challenge is to win titles and trophies with Real Madrid," Modric said.
"I have trained, I have worked hard and I have played 25 minutes with Croatia. I hope that I only need a couple of games to be fit and to reach the highest level. I have everything that I want. Now i just want to enjoy my football, improve my qualities and help the team win everything."
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