Twenty leading figures in world football allegedly accepted a million dollars in bribes to 'fix' the election for the game's top job.
They each received $50,000 (£31,000) from the ruler of a Middle Eastern state - who had the money flown in by private jet - to back Sepp Blatter as head of Fifa.
Envelopes stuffed with cash, it is claimed, were their reward for ensuring Blatter beat Lennart Johansson, the 'honesty' candidate, to become the soccer world's most powerful leader.
Johansson last night demanded that Fifa investigate the claims, which threaten to plunge soccer's governing body into a corruption scandal like that enveloping the Olympic movement.
Johansson, the Swedish president of European football's ruling body, urged Fifa to follow the International Olympic Committee's example by holding an internal probe. 'When things go wrong like this, sort it out. Let's have an investigation for the good of the game', he told The Observer.
But Johansson, in London for today's Worthington Cup final at Wembley, said he did expected Blatter to reject such a move. 'I have reasons to ask myself: why should they be against it? I think Blatter should have an inquiry.'
The allegations appear in an explosive book about Fifa which, as The Observer revealed two weeks ago, Blatter is trying to have banned.
How They Stole the Game, by British author David Yallop, has sparked calls for an independent inquiry into alleged sleaze at Fifa.
But Blatter's bid to suppress the book suffered a setback last week when a Dutch court refused to grant him an injunction to stop it being sold in Holland.
The Amsterdam judge heard that Yallop's charges were serious enough to warrant an inquiry. He suggested that Fifa should act finally to clear up claims that the presidency contest was rigged.
However, Blatter has dismissed that idea out of hand, saying: 'Why should I? I cannot open an inquiry into myself. The elections are now finished.'
Dutch judge Orobio de Castro said that Yallop was entitled to ask why so many Fifa delegates from African countries suddenly switched their support to Blatter from in the election last June.
The judge decided that Yallop's claim about envelopes of cash and the Middle East leader, who cannot be named for legal reasons, 'is sufficiently concrete that Blatter and Fifa can defend themselves against it.' He also suggested that the 20 delegates who unexpectedly changed sides and the wealthy figure said to be behind the vote-buying 'could be asked about the sequence of events.'
How They Stole the Game asks what became of the billions of dollars Fifa earned from selling World Cup television rights, highlights Fifa leaders' extravagant lifestyles, and discloses details of secret accounts overseas.
Judge De Castro defended Yallop's right to probe Fifa's financial arrangements. 'It can be expected of an organisation of such size and such public importance that its policy in these areas is transparent,' he said.
'In the absence of such transparency, it cannot justifiably complain if critical questions arise among the public and if doubts are publicly expressed about the provenance and expenditure of money.'
Yallop's book purports to reveal the sensational details of how Blatter, the Swiss underdog, managed to beat the favourite, Johansson.
It does not claim that Blatter was either involved in or knew about the alleged vote-buying. But it does allege that the Middle Eastern figure flew $1 million to Paris, which was given to around 20 Fifa delegates at the Meridien Hotel.
The author, best known for his five-million-selling In God's Name - an exposé of corruption inside the Vatican - instead says that associates of Blatter 'fixed' the poll.
Johansson voiced his suspicions immediately after he lost the presidency poll, by 111 votes to 80.
David Will, the Scottish vice-president of Fifa, told The Observer: 'There were plenty of rumours going round about the presidential election, but I don't know if the claims of supposed malpractice are true or untrue.
'I've no reason to believe these rumours or disbelieve them.' Will does not back any sort of inquiry.
Yallop said last night: 'Fifa won't have the investigation because too many people implicated in corruption going back 25 years are still in positions of power.'
He wants an independent probe along the lines of the IOC investigation conducted by Senator George Mitchell.
With British companies running scared of publishing Yallop's book here, the author is now considering publishing it himself.
Although Blatter succeeded in having the book banned in Switzerland, it is being sold openly in Germany, Austria and Brazil.