Jordaan told a news conference that Africa's first edition of football's biggest tournament was the culmination of a journey that began with Mandela's release and then the first multi-racial elections in 1994.
"When Nelson Mandela walked out of the prison, we were all debating the kind of South Africa that we will create from 1990 onwards and as we sit in 2010 and we see the arrival of the teams, we can say truly this is the kind of South Africa we hoped for, that we dreamed of," he said.
"The people are where we wanted this nation to be," Jordaan added, citing the historic staging of two major rugby matches over the last two weeks in Soweto, the sprawling black township that was central to the anti-apartheid struggle.
Rugby is traditionally the game of South Africa's white Afrikaners, the backbone of the apartheid system, but they mixed happily with black inhabitants of the township during last Saturday's Super 14 rugby final and the semi-final a week before, held in the new Orlando Stadium.
FIFA President Sepp Blatter, who has steadfastly supported holding the World Cup in South Africa despite legions of sceptics and critics, joined in the hyperbole.
"This first African FIFA World Cup will be a big page in the history of humanity, not only in the history of sport," the head of football's governing body said in a statement after a meeting of the World Cup organising committee.
Jordaan, who hopes that the World Cup will have a powerful impact in bringing the races together in a country where they are still often divided, said the tournament would be an intense emotional and human experience, not only for South Africans but for all the teams and foreign fans.
"That is what is going to be special in this World Cup," he said, adding that a successful tournament would bring more investment and tourism to Africa's biggest economy.
"There has been a complete turnaround of the doubters, who are now believers. Those who questioned are followers and how the mood has changed is just wonderful to see," he added.
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