Mr Brown is in Beijing with his wife and their two young sons, John and Fraser, for the last few days of the Games and for the closing ceremony on Sunday, when the Olympic flag will be handed to London's mayor Boris Johnson.
He went on to meet young athletes at the Olympic athletic lodge and will be discussing how Britain can build on its Olympic successes in Beijing - where Team GB is currently third in the medal table with 18 golds.
Later he said Britain was "so delighted and excited" by the sporting success of the Olympics "that what we want to do is to turn what has been two weeks of sporting success into ten years of sporting triumph".
He said the programme of elite funding for athletes in the run-up to 2012 was being doubled "so that more and more athletes who are potential winners in 2012 can get the sort of support that our cyclists and others have been getting over the last few years".
Earlier sports minister Gerry Sutcliffe, who famously bet his Australian counterpart Kate Ellis that Britain would outstrip Australia in the medals table, said it was not over yet.
The two rivals are currently neck-and-neck in terms of overall medal haul - although Britain is ahead on golds.
Mr Sutcliffe told BBC Radio 4's Today programme earlier: "We have got a couple more days to go so I'm not counting my chickens yet but it's been a fantastic experience."
Mr Sutcliffe and Ms Ellis agreed that the loser would agree to wear their rivals' national colours to a major sporting event in their own country.
Ms Ellis has been quoted as saying she was "getting pretty nervous" and hoping Australians could clinch a few more medals.
Francis Adamson, Australia's acting high commissioner, told the BBC Britain was probably "uncatchable" on golds but she "still had some hope" on the overall tally. Asked if Ms Ellis would wear a red, white and blue shirt if they lost, she added: "Australians never welch on bets".
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