The Nobel Peace Prize laureate had told South African organisers that he would only support a bribe-free South African bid, Danny Jordaan told the CNN Global Forum.
"Then we had our first meeting with the FIFA executive and Archbishop Tutu said: If you vote for us, I will make sure that you get a first class ticket to heaven," Jordaan quoted him as saying.
"I kept quiet and when we went out, I said: Arch but you said we must not bribe. Isn't that a bribe?.
"He said: No, no, it's not a bribe. A bribe is only when you give things to people who are alive. In order to get their first-class ticket, they must first die. That's not a bribe."
Jordaan also paid homage to South Africa's first democratic president Nelson Mandela, who travelled the world to support the continent's first tournament which was granted in 2004.
"Madiba... his hands, his fingerprints, are all over all of these events," Jordaan said, referring also to the 1995 rugby World Cup which was seen as a racially uniting force in the country.
Mandela was in Zurich when South Africa's successful bid was announced six years ago.
"It was such an emotional moment for him and Archbishop Tutu. We have photos where he started dropping some tears and Archbishop Tutu took out his handkerchief to wipe off the tears.
"It was just incredible these two human beings who travelled the world with us."
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