The new indoor complex, consisting of a 90-metre, six-lane running track, long and triple jump pits, a hall for pole vaulting and the high jump, plus a weight training facility, will bolster the school's already legendary sporting facilities.
Eton College already has two swimming pools, 30 cricket squares, 24 football, rugby and hockey pitches and a gym.
Derek Casey, chief executive of the Sports Council, which is providing pounds 3m towards the facility, said the centre would be for the benefit of the whole community in surrounding Berkshire.
"We never forget where lottery money comes from - that's the community and it will go back into the community," said Mr Casey. "Eton College will get some benefit from the new centre but to say that we have given them a grant is absolute nonsense. The new centre is for the community. Since the college has given the land and is helping to fund the project, there will be some benefit to them, that is all."
However, Steve Osborn, director of the Safe Neighbourhoods Unit, which recently produced a report on the role youth and sporting facilities can play in crime reduction for the Joseph Rowntree Foundation, said that the decision was "staggering".
"I'm surprised at the grant, particularly when you consider that for the last five or six years there has been a substantial reduction in youth services by local councils across the country. In many cases youth projects that are known to be effective in reducing crime have been closed," said Mr Osborn.
Berkshire has one of the lowest unemployment rates in the country and its residents earn more than the national average. Eton and the surrounding villages and towns are some of the county's most exclusive.
Eton is paying pounds 200,000 towards the cost of the complex, is donating 11 acres of land and is also throwing in a 400-metre running track, which will be upgraded, also with lottery money. In return, Eton pupils, whose parents pay more than pounds 4,000 a term, will be allowed to use the complex exclusively in the day for free.
The Sports Council grant is to cover the majority of the building costs and two local authorities are chipping in pounds 1m.
Roderick Watson, bursar at Eton, also said that the facility would benefit the whole community. He said it would "hardly be exclusive" because, he claimed, the catchment area includes west London and would be open to the public. Admission charges, he said, had not been decided but would be subsidised by the two local councils, Windsor and Maidenhead, and Slough.
Mr Watson said that the public would have access to the complex for about 80 per cent of the time, and local clubs would benefit greatly from the improved facilities.
The Windsor, Slough and Eton Athletic club will benefit from the centre. The club, which has produced some of the country's finest athletes, is "deprived" according to Mr Watson because they do not have a world-class running track and facilities to train with.
Undue press attention on the complex, he said, could "poison what could possibly be an excellent blueprint for the future development of sporting facilities elsewhere."
Last night, the Labour Party declined to comment on the new complex at Eton.
More National Lottery cash was also provided for other sporting facilities yesterday by the Sports Council. A new pounds 4.8m complex will be built in Hackney in east London, and a total of pounds 20m will be spent on 136 schemes across the country.