The 28-year-old Dutch international, told by Barcelona in May he could leave the club despite having another year to run on his contract, has signed a three-year deal with the premier league side.
"He's high-profile, a dazzling player. If he reaches anything like his potential he will be popular here. If he does well he will be an icon almost immediately," said Robson, who compared his signing to that of Alan Shearer in 1996.
"It's very similar to the feeling in the city when the club decided to bring Alan Shearer back home in 1996.
"Patrick's a player of immense experience and of great stature, an international of top repute who has played for the top clubs.
"I think he's got the best years of his career ahead of him. He will be one of the most significant signings that Newcastle have made for many years.
"To get him for nothing is magnificent. There have been 25 million and 10 million fees banded around and we have been very frugal in our dealings.
"I think the fans will be delighted, thrilled and enthused."
Kluivert, who suffered an injury-hit final season at Barcelona and failed to make an appearance for the Netherlands during their run to the semi-finals of Euro 2004, said he was delighted to finally test himself in England.
"The Premiership is one of the most competitive leagues in the world," he said. "I have won prizes in other countries and now I'm feeling 100 percent fit and I hope that I can win very big prizes with Newcastle.
"That is possible with all the players that I will be alongside in our team. I am also happy to be joining a club with lots of perfect young players, that's very important to me."
Kluivert, who spent six years at Barcelona after joining from AC Milan, is expected to edge out Welshman Craig Bellamy as skipper Shearer's strike partner.
"I'm looking forward to playing alongside Alan Shearer or the other two strikers," said the Dutchman who was a product of the Ajax Amsterdam youth academy, scoring the winner as a teenager in their 1-0 Champions League final victory over Milan in 1995.
Kluivert, who will wear the number 11 shirt at Newcastle, is the record scorer for the Netherlands with 40 goals since making his international debut in 1994.