Prime Minister David Cameron yesterday promised £125 million a year over the next four years to help athletes inspired by this year's medal haul to emulate the feat in Rio in 2016.
The Scottish Government, meanwhile, revealed it is providing an additional £8m a year to support Scotland's elite athletes ahead of the Glasgow Commonwealth Games in 2014.
Mr Cameron, who revealed the UK-wide funding would come from both the Treasury and the Lottery, said the past fortnight had proved that Britain's "time has come" and a renewed national confidence would confound those who suggested Britain was "down and out".
"Over the last couple of weeks we have looked in the mirror and we like what we have seen as a country," he added, saying the public had proved itself "the greatest member of Team GB".
Praising athletes, volunteers and politicians of all parties involved, he added: "Take all of this – the attitude, the confidence – and you see what Britain is today: sure of who we are, proud of who we are. In short, not a country whose time has been but whose time has come."
The sport funding is part of the legacy officials said would be created after the winning bid to stage the Games.
The Prime Minister added: "Nothing has been more inspirational than seeing our elite athletes win gold this summer.
"There's a direct link between elite success and participation in sport. I want one of the legacies of these Games to be our athletes triumphing in Rio in 2016, and in future Olympic Games."
A Scottish Government spokesman said its investment was aimed at improving sport in Scotland as the country prepares for the Commonwealth Games.
He added: "We're increasing investment in PE. Our active schools network is a huge success, opening up five million sporting opportunities for young people to try sports, and we are opening up schools to become community sports hubs to provide a healthier and more active Scotland."
Sir Chris Hoy, whose emotional sixth gold medal win was described as the defining moment of the 2012 Games by Jacques Rogge, president of the International Olympic Committee, said Lottery and government funding had helped him achieve his dreams.
The cyclist said: "I am old enough to remember a time when things were run on a shoestring budget before National Lottery and government investment transformed British Olympic sport.
"Having these guarantees for the future will be a huge boost for all the athletes aiming to win medals at Rio 2016."
As he announced the sport funding, Mr Cameron also thanked Olympics volunteers, the Armed Forces, police and others who made the Games possible, describing them as "the very best of Britain".
Earlier, US President Barack Obama called Mr Cameron to congratulate him and the people of the UK on the success of the Games.
A White House spokesman said: "Both leaders commended the exceptional performances by both the Olympic teams of the United States and Great Britain and noted how proud we all are of them."
Prince Harry also hailed the the Olympics as an "extraordinary" event. In a guide to the closing ceremony, which he is attending as representative of the Queen, he said: "The London 2012 Olympic Games will stay in the hearts and minds of people all over the world for a very long time to come."
Meanwhile, security company G4S, which attracted controversy after it failed to train enough staff and the Army had to be called in, yesterday said it was contributing £2.5m to Armed Forces charities as a goodwill gesture.
The UK Government is also set to issue a commemorative coin to thank the Armed Forces and police for their work in delivering the Olympics.
A commemorative baton will also be given to the 18,000 volunteers who worked as London and UK ambassadors.
The Prime Minister also revealed that London 2012 organiser, Lord Coe, is to continue his involvement with the Olympics as a "legacy ambassador", advising on the best ways to secure long-term benefits for the UK.
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