Bid chairman Lord Coe said his team had won "the biggest prize in sport" as London was chosen to host the 2012 Olympic Games.
The presentation led by Coe helped London beat Paris in a vote by International Olympic Commitee members.
Coe told BBC Sport: "It is the most fantastic opportunity to do everything we've ever dreamed of in British sport.
"We have a chance over seven years and way beyond that to change the face of British sport."
London's team survived into the last round of voting after Moscow, New York and Madrid were all eliminated.
It then won by four votes against Paris to bring the Olympics back to Britain for the first time since 1948 - and make London the first city to host the modern Games three times.
The Games will be held in late July and early August 2012, according to Lord Coe, who said winning the right to host was "almost entirely on a different planet" to claiming a gold medal of his own.
Coe paid tribute to his fellow bid team members for their part in the triumph.
"Everyone was all together and we never lost our confidence. We just recognised we could do it in a very special way and we will do," he said.
And he added: "I always knew this was going to be close. I am absolutely ecstatic. This is our moment, the spin-off for sport in the UK will be huge."
London Mayor Ken Livingstone, also part of the bid team, said: "When we started out we felt there was a mountain to climb and we would never win.
"But what came over in our presentation is that the Olympics is about giving kids a chance - this is about kids.
"We spent a lot of time working out the finances and getting a plan - we will start work tomorrow, we already have some of the facilities."
Culture Secretary Tessa Jowell, who will now become Olympic Minister, said: "When we were waiting for the final result there were 30 kids here with us from east London.
"I said 'how many of you are going to go for gold medals?' and they all put up their hands. That is what this for - to unlock their ambitions and their dreams.
"This is the biggest prize that sport can bestow and we have won it for London. I want to thank everybody at home who kept faith with this because they have made the difference."
Sports Minister Richard Caborn said: "I was surprised when London came out, no doubt about it, purely because all the photographers were down with the Paris delegation."
Caborn also paid tribute to Tony Blair's involvement, saying: "This is a guy who is chairing G8 and he came here and that was impressive, and impressed the IOC council."
IOC president Jacques Rogge said London would deliver a "superb" Games.
He said: "It was one of the results I expected. I always thought it would be a close final between London and Paris.
"They asked me for my thoughts this morning and I thought it would be decided by half a dozen votes. We knew the two bids were very, very close.
"Well done London. It will be a superb Games and will strengthen the Olympics.
"Paris put in a very strong bid and I understand their disappointment but that is the nature of sport."
Rogge attended a media conference after the decision at which the official contract for London to host the Games was signed.
Rogge said: "I first met Seb Coe in 1980 when he won his gold medal - we couldn't have believed at this time that 25 years later we would sign the host city contract."
Four-times Olympic gold medallist Matthew Pinsent admitted he was not feeling positive in the moments before the decision was announced.
"I was sure when he (Jacques Rogge) opened the envelope it would say Paris," Pinsent said.
The Princess Royal had earlier opened London's final presentation, reading a message from The Queen, and she said afterwards: "It's very special for London.
"What they were impressed with was we sold it to them as being good for the Olympic movement. There is nobody on that (bid) team who isn't articulate and throroughly committed."
Craig Reedie, the British Olympic Association chief, said: "This has been the most competitive race in Olympic history and we should be rightly proud that Britain has won."
Former Olympian Colin Jackson, in Singapore with the bid team, said: "It was incredible - we all just froze and then there was huge uproar. It was one of the best feelings I have ever had.
THE LONDON PRESENTATION
Princess Royal: Read message from Queen looking forward to 2012
BOA's Craig Reedie: "We understand the recipe for magical games"
Lord Coe: "London's vision to is reach people, young people, all around the world"
Video of the venues presented by Sue Barker
Denise Lewis: "Every athlete will leave with friendships and memories"
London Mayor Ken Livingstone: "London welcomes people with open arms and open mind"
Tony Blair: "Our vision is to see millions more young people participating in sport"
Tessa Jowell: "Our vision is to serve ambitions of Olympic movement"
Lord Coe returns: "We share a common goal for the future of sport"
"I was shocked when the news came - I just turned round and grabbed Jonathan (Edwards) and we just hugged like schoolchildren.
Jonathan Edwards said: "We were worried we might go out in round three - we thought our best chance would be if we went head-to-head with Paris in the last round and we got Madrid's votes.
"But in fact we were ahead of Paris after the third round, and Paris got two more (17) of Madrid's votes than we did (15). I feel proud to be British."
England football coach Sven-Goran Eriksson and his captain David Beckham accompanied the bid team to Singapore.
Eriksson said: "It's an exciting day and a long day but the presentation London did this afternoon was absolutely top class.
"London is my city now. I live there and work there and I am very, very happy."
Beckham, who was born and raised in east London, already knows the River Lea where some of the water sports will be held.
"I was saying last night I used to canoe on the Lea River. The whole area is going to be transformed," he said.
"It's not just about the east end - it's not just about London. It's going to transform the whole country. To have the Olympics in London - that's something special."