The 21-year-old, who joined for $30 million from Santos, juggled for some 8,000 ecstatic fans at the Bernabeu stadium.
Balancing one ball after another on his back, flicking them over his shoulder and then kicking them into the stands, Robinho had to fend off a stream of admirers who ran on to the pitch to embrace him.
"Today we are going to present one of the great players in the world," said Real Madrid president Florentino Perez.
"Football can be many things but one of the most important is the spectacle it provides, and it is in this aspect of fantasy football that Robinho excels.
"It hasn't been an easy road for him to come to Real Madrid, but I think he's chosen the perfect team and the perfect league for him to demonstrate is skills. Robinho's Real Madrid dream begins here."
The presentation generated the level of interest seen when Galactico predecessor David Beckham signed for the club in 2003.
RELAXED ROBINHO
Looking calm and relaxed Robinho was presented with the number 10 shirt worn by Luis Figo last season.
"I'm very happy to be here at Real Madrid, a club with such history and tradition and one that has such excellent players," he said.
"I would like to thank the people for the wonderful reception I've been given and it's great to have so many team mates who play for Brazil here at the club."
Robinho burst on to the scene as an skinny 18-year-old by helping Santos win their first Brazilian championship in 2002.
His trickery, skills and physique have led to comparisons with former Santos great Pele although the youngster has yet to be fully tested against the world's top defenders.
The forward could end up forming an all-Brazilian front line at Real with Ronaldo and Julio Baptista. He said he was confident he would make a rapid transition to European football.
"Brazilian football is spectacular and entertaining and a lot of its players have succeeded here and I want to do the same. There are a lot of similarities between Spanish and Brazilian football and I hope to adapt rapidly," Robinho said.
TRADEMARK STEP-OVERS
"I hope to use a few of my trademark 'pedaladas' (step-overs) against my opponents while I'm here," he added with a smile. "But above all I want to help make Real Madrid a champion team and win a lot of trophies."
Robinho is the fourth Brazilian international in the Real squad and will be reunited with former Santos boss Vanderlei Luxemburgo who is now in charge of the nine times European champions.
"It is good to have so many team mates who play for Brazil here at the club," he said. "I'm fit and raring to go and when Luxemburgo decides to select me I'll be ready to play.
Arch-rivals and Spanish champions Barcelona who have six Brazilian-born players on their books including World Player of the Year Ronaldindo.
Robinho, who scored twice in his final home match for Santos on Sunday, said he hoped he would bring something different to Real Madrid.
"Ronaldinho is a good friend and he's considered the best player in the world. But he has his style and I have mine and I hope I'll make my own mark when I'm here."
