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The unexpected star of the World Cup finals, Colombia’s James Rodríguez, has signed for Real Madrid for a reported £63m.

The 23-year-old follows the signing of another key midfielder from the World Cup, Germany’s Toni Kroos who joined for a bargain £20m, and will be given the No10 shirt which was last worn by Mesut Özil.

He passed a medical in the Spanish capital on Tuesday morning and has agreed a six-year deal at the Bernabéu. He was presented to Real Madrid’s fans in their stadium on Tuesday night.

He emerged to a rapturous reception from a 45,000-strong crowd, around a third of whom were wearing Colombia shirts.

Then while he kicked balls into the crowd – as is traditional for new high-profile arrivals to do – he was rushed by several enthusiastic supporters and made a point of embracing them before they were ushered away by security.

He said: “I’ve always followed Real Madrid and always dreamed of playing here. I’ve suffered a lot to get here and when you do that then it tastes so much better.

“I will never forget this day. I hope to work hard, to train well, and to experience a lot of joy here. I know I am under a lot of pressure, but I am happy to face it.”

The fee makes Rodriguez the fourth most expensive transfer of all time after Real’s £86m for Gareth Bale and £80m for Cristiano Ronaldo, and Barcelona’s £75m for Luis Suárez.

“The numbers mean nothing to me,” he said. “I just want to help make history and bring joy to the Madrid fans.

“This is a club which is used to winning and I’m prepared mentally and physically to do so. It is a pleasure to be among so many stars and I’m sure I’ll learn a lot from everyone.”

Rodríguez was one of the revelations of the World Cup, scoring in each of Colombia’s games as they reached the quarter-finals of the competition for the first time, eventually losing 2-1 to the hosts Brazil.

He scored six goals at the World Cup to finish as the leading scorer – one clear of Thomas Müller – while his 25-yard volley against Uruguay was voted goal of the tournament.

Rodriguez gives the thumbs up at his medical. Photograph: Pedro Castillo/Real Madrid via Getty Images

Rodríguez began his professional career with the Colombian side Envigado before moving to the Argentinian club Banfield aged 17. His performances attracted the attention of Porto, who signed him for £4m in 2010, and three years later he joined Monaco for £38.5m after helping the Portuguese side win a hat-trick of league titles and the 2011 Europa League.

The left-footed forward scored 10 goals in 38 matches in all competitions for Monaco last season as they finished second in Ligue 1 behind Paris Saint-Germain.

Rodriguez's volley against Uruguay was voted goal of the World Cup. Photograph: Felipe Dana/AFP/Getty Images

Monaco said they had not been looking to sell Rodríguez but described the deal as “one of the most significant transfers in football history”.

“The club would like to take the opportunity to thank James for the role he played in getting the club back to the Champions League and wishes him the very best for the future,” they said.

“The club had no intention to sell the player, however the time came when the solution of a transfer was considered to be the most beneficial solution for all parties.

Facebook Twitter Pinterest A fan is grabbed by security guards as he tries to embrace the new Real Madrid player James Rodríguez Photograph: Daniel Ochoa de Olza/AP

“Monaco is proud to be a party to one of the most significant transfers in football history. Monaco is a club that will continue to grow and remains focused on the future. More than ever it has the ambition to strengthen the team and continue to progress for next season.”

The announcement had been delayed as Real and Monaco struggled over the small print in the deal with Monaco’s owner Dmitry Rybolovlev holding out for €85m, according to L’Equipe.

Monaco were keen to sign Diego López in part exchange but the goalkeeper did not want to leave. Real are expected to sign the Costa Rica goalkeeper Keylor Navas for £8m as their No1 after the European champions agreed to meet the release clause in his contract at Levante.