Mr Stofile told Business Day that Mr Mandela had written a letter to Danny Jordaan, the CEO of the World Cup local organising committee, and "demanded" tickets to the opening match.
"He himself demanded to be part of the opening match, and the local organising committee said fine," Mr Stofile said.
"When we read his letter to Danny Jordaan, there was no discussion. For us this was natural because if you are looking for someone who was responsible for bringing the World Cup to SA, look no further than him (Mr Mandela)."
Fifa president Sepp Blatter had said earlier in the day that he was spending sleepless nights agonising over whether "the most charismatic humanist alive" would be able to be part of the 94000-strong crowd that will descend on Soccer City, near Soweto, next week.
Mr Blatter had said there would be something missing from the start of the tournament if Mr Mandela's frail health prevented him from attending. It seems now the Fifa president will be only too happy to accommodate Mr Mandela.
Mr Stofile said Mr Mandela had requested tickets only to the opening match but they would be ready to accommodate more requests should he want to attend other matches.
"If I were the president of Fifa, I would give Mandela the freedom of the World Cup and allow him to attend all the matches," Mr Stofile said. "But he is an old man and I do not think that he would want to do that. But you never know with the old man, you never know."
He hinted that US President Barack Obama could still make a surprise visit to SA and attend the opening match .
US Vice-President Joe Biden will attend the opening ceremony on June 11 and will be accompanied by his wife, Jill.
The vice-president is also expected to watch the US's opening match against England in Rustenburg and many believe this was the strongest sign that Mr Obama himself would not make the trip to SA.
But it is possible Mr Obama may still show up and that his visit has not been announced officially for security reasons.
"So you never know and we will have to just wait and see if he will indeed attend the tournament," Mr Stofile said.
Mr Blatter raved about Soccer City and said it was one of the best stadiums he had seen in his life.
"I have to say it is a five-star stadium and can be compared, if comparison is possible, perhaps with Wembley Stadium in London.
"Yes, this is called the Fifa World Cup but who did the homework? Who made all the preparations for this World Cup?" he asked.
"Who built all these beautiful stadiums that we are marvelling at in this country ? It is you South Africans. It is you."
To recognise the contributions made by Johannesburg as one of the host cities of the World Cup, a commemorative plaque was unveiled at Soccer City by Mr Blatter, Mr Stofile, organising committee chairman Irvin Khoza and Confederation of African Football president Issa Hayatou, among other officials.