The successful resolution to negotiations brings to an end one of the most protracted transfer sagas of the summer transfer window, with the constant haggling between the two clubs over a fee threatening to scupper the switch.
Modric had agreed personal terms with the Santiago Bernabeu outfit beforehand, but Spurs chairman Daniel Levy's financial demands initially proved problematic, a circumstance that the 27-year-old acknowledged with regret.
"It has been a really long process and I've missed two games," the Croatia international said regretfully at his official unveiling.
"I have been training with Tottenham's fitness coach, working hard as well as playing for Croatia. I hope I will only need a couple of games to get fit and reach my peak fitness level and that expected of me by Real Madrid."
|"I have been training with Tottenham's fitness coach. I hope I will only need a couple of games to get fit"
- Luka Modric
The creative midfielder then spoke of his enthusiasm regarding the prospect of playing under coach Jose Mourinho, insisting that he is up to the challenge of playing on the greater stage.
"I'm happy, honoured and proud to be at the biggest club in the world," Modric enthused. "When I realised that Real Madrid wanted to sign me, I was excited that such a big club were showing an interest in me."
|16/1||Tottenham are 16/1 with Bet365 to draw 2-2 with Norwich City|
"It will be difficult but I think I have the quality to play here. I have set myself the challenge of winning trophies with Real Madrid."
Indeed, Mourinho will be hopeful his latest signing will spur on the Blancos in the club's already-stuttering title defence, after seeing his men only collect a single point in their opening two Liga fixtures.