Real Madrid have completed the signing of Croatia playmaker Luka Modric from Tottenham Hotspur as the stuttering Spanish champions seek an injection of guile and creativity to get their troubled season back on track.

Modric flew into Madrid on Monday morning and after passing a medical signed a five-year contract in the presence of big-spending Real president Florentino Perez before holding a news conference at the Bernabeu stadium.

The 26-year-old, who will wear the number 19 shirt, said he was relieved the protracted transfer negotiations had concluded before the transfer window closes on Friday and he was prepared to fight to win a place in Jose Mourinho's team.

"I have to work very hard to earn a spot in the starting eleven and I'm prepared to do it," he told reporters as his wife and young son looked on.

"I've come here to improve every day and to win titles with Real Madrid. These are my personal goals," he added.

"I believe I have what it takes to play here. I've got everything I need and I want to enjoy football and to learn.

"I'm grateful to Tottenham, but I'm now opening a new page in my life."

While neither club gave financial details, Spanish media reported Real would pay 35 million euros ($43.81 million) for Modric, plus another 7 million depending on the number of his appearances and the team's performance.

His arrival in Madrid may help Real put a poor start to the season behind them, during which they have taken one point from two La Liga outings and lost Thursday's first leg of the Spanish Super Cup 3-2 at Barcelona.

They crashed to a shock 2-1 defeat at city rivals Getafe on Sunday, which prompted a rare burst of public criticism of his underperforming players from a furious Mourinho.

Real have a chance to reignite their season in Wednesday's Super Cup return leg at the Bernabeu when Modric hopes to make his debut.