His club, Santos, had been demanding a $50m (£28.5m) penalty to release the player, who has a contract with them until 2008. But Robinho's agent, Wagner Ribeiro, said the player had agreed to waive the 40 per cent to which he was entitled, so substantially reducing the transfer fee.
The 21-year-old, who was an ever-present in the Brazil team which won the Confederations Cup in Germany last month, said a move would help him to protect his family. His mother was kidnapped for 40 days at the end of last year.
"Robinho is just waiting for a transfer certificate to travel. He waived the 40 per cent to which he was entitled to be able to fulfil his dream of playing for Real Madrid," Ribeiro said.
Robinho, who came to prominence as an 18-year-old, when he helped Santos to win the Brazilian championship, has been the subject of speculation over a move to Real for almost a year. He was also linked with Arsenal and Chelsea.
His skills and physique have often led to comparisons with Pele, who spent most of his career at Santos, although the youngster has yet to be tested fully against the world's top defenders.
Robinho has been at loggerheads with Santos since the end of the Confederations Cup when he said he was close to signing a deal with Real. The Santos president Marcelo Teixeira accused the Spanish side of approaching the player without his club's consent and said a deal would only de done if the $50m penalty was paid.
But, after returning to Brazil, Robinho defied orders to go back to the club and missed 12 training sessions and three matches.
Spanish media reported yesterday that Robinho had undergone a medical check-up at a clinic in Sao Paulo before signing for Real and his imminent move was later confirmed on the club's website.
Robinho made his international debut in a World Cup qualifier against Bolivia last year and scored his first goal in a friendly against Hong Kong in February.
He has made 12 international appearances, scoring four goals.Reuse content