The Greek capital saw off the challenge of four other bidding cities, including the pre-vote favourite Rome, by a margin of 25 votes. The last time any city bettered that margin was when Berlin beat Barcelona to the 1936 Games by 43 votes to 16. Since then, the International Olympic Committee has grown to 107 members, and the secret ballot taken in Lausanne awarded Athens the Games ahead of Rome by 66 votes to 41. Cape Town, Stockholm and Buenos Aires all fell in earlier rounds.
Six years ago the Greeks sought the 1996 Games with a bid which was guilty of hubris. They were outflanked by the energetic efforts of Atlanta.
But after the widely felt weaknesses of Atlanta's effort last year, notably its excess of commercialism, the opportunity was there for Athens , which hosted the first modern Games of 1896, to profit from the idea of returning the Olympic Movment to its roots. This they did.
"The extra vaule of the Greek tradition made the difference," said Jacques Rogge, an IOC member.
Dick Pound, IOC executive board member, added: "They corrected their mistakes. They were totally focussed on the quality of the bid rather than demanding the Games as a right."
Craig Reedie, one of Britain's two IOC members, commented: "There is a natural sympathy for Greece. If you go with your heart, rather than your head, you vote for Athens."
The trauma of 1991 left Greeks weeping on the streets. Last night the tears flowed in the Piazza Navona, where Romans watched the voting on live television.
Not every Roman was dismayed. "I am absolutely delighted," said Cristiano Brughitta, spokesman for the Campaign against the 2004 Games in Rome. "I am just pleased to have spared our town this huge disaster."
The factors presenting a problem for Athens were the same which faced Rome - difficulties with transport, pollution and accommodation.
Athens has planned to get round some of these difficulties by building a new Metro system and 65 extra miles of motorway which will divert traffic away from the crowded city centre towards the Olympic facilities already largely existent to the north of the city.
Each of the five bids were supported in Lausanne by high-profile personalities. Buenos Aires was backed by the Argentine president, Carlos Menem; Rome had Luciano Pavarotti in their line-up; Stockholm had Bjorn Borg.
Gianna Angelapoulos-Daskalaki, the exotic and impressive president of the Athens bid, had travelled the world to promote the claims of her native city. Angelapoulos, who has a home in Chelsea and a wealthy industrialist husband, has been described as a cross between Melina Mercouri and Mrs Thatcher. But her charm was wasted on Primo Nebiolo, the president of the Rome bid, when the two met at last month's world athletics championships in Athens.
Nebiolo, president also of the International Amateur Athletic Federation, refused to shake hands and turned away. His subsequent statement that the Greeks were incapable of organising major sporting events was not supported by the facts - the IAAF world championships were very well organised this year.
As the IOC members witnessed final presentations yesterday from each of the five bidders in Room 280 of the Palais de Beaulieu, several questions hung in the air.
Would Nebiolo's criticisms prove counter-productive for Rome? Would the sequence of bomb attacks in Sweden blow a hole in Stockholm's challenge? How strong was the guilt over Athens? And what emotional charge would be carried in the personal appeal by South Africa's President, Nelson Mandela?
The result was definitive. Nebiolo complained afterwards that Rome had suffered through an accord worked out on Thursday night between Cape Town and Athens, whereby the Greek city received support this time round in exchange for votes supporting Cape Town with its expected bid for the 2008 Games. After Cape Town had gone out in the penultimate round with 20 votes, Athens picked up 14 of them in the final count.
The result also means Britain, which is committed to bidding for an Olympics in London in the near future, will almost certainly go for the 2012 Games rather than those of 2008, given that the event is not likely to be hosted on consecutive occasions by a European city.
Simon Clegg, the chief executive of the British Olympic Association, said: "We will hit them once with a bloody impressive bid," he said.
Why there is no catching Africa's runners, page 23