Finland, Sweden and the US have already selected sites for permanent disposal, and construction of the Finnish facility has been underway for several years.
Successive UK governments commissioned reports but failed to make decisions on the issue.
Two years ago, the Committee on Radioactive Waste Management (CoRWM) recommended deep geological storage for the waste now languishing at more than 30 sites around the UK, including power stations, research laboratories, and military facilities.
CoRWM recommended that communities should be invited to volunteer as hosts, a model that worked effectively in Finland; and the government has already indicated its agreement with that principle several times.
The Managing Radioactive Waste Safely white paper spells out the details.
"The government, along with the Nuclear Decommissioning Authority, will be looking to sit down and discuss, with any community that feels it has an interest, both the technical aspects... and the wider social, economic and environment issues involved," Environment Secretary Hilary Benn told MPs.
"Ultimately, for the process to succeed, a mutually acceptable agreement will need to be reached."
The community finally chosen to host the waste would gain economically through the creation of new jobs, but could also receive funds from the government - which opponents of the scheme characterise as "bribery".
"In the surreal world of Labour's nuclear obsession, waste dumps are now being presented as an economic opportunity," said the Scottish National Party's Westminster energy spokesman Mike Weir.
"A nuclear dump will require exceptional levels of security for thousands of years. What sort of blight and legacy is that for a local community?"
Any proposals to store waste in Scotland would be dealt with by the Edinburgh parliament, and the current Scottish government has made clear its opposition to hosting either a deep disposal site or any new nuclear reactors.
The Welsh Assembly has also "reserved its position", citing concerns over security, and will not be asking local authorities in Wales to bid.
The British Geological Survey would assess proposed sites to make sure they are stable.
It may take 10 years before a location is finally agreed, the government believes, and a further 10 before the first consignments of waste are stored away.
No new money
The price for disposing of the country's nuclear legacy - which will be paid from government funds - is not clear.
But the government says waste from any new power stations would be borne by the industry itself.
"We've tried to devise a formula which makes sure the taxpayer is protected from any costs arising from the decomissioning and disposal of [waste from] new nuclear stations," Mr Hutton told BBC News.
"The new nuclear waste - all of it - will be paid for by the nuclear industry."
That claim is disputed by anti-nuclear campaigners, who believe that the recent nuclear white paper leaves the door open for public subsidy.
Speaking at his monthly media conference, Prime Minister Gordon Brown said the world may need another 1,000 nuclear power stations to bolster energy security and fight climate change.
But some key resources, including skilled engineers, mean there is likely to be competition between countries if there is a worldwide surge in reactor construction.
The government organised a day-long seminar in London attended by leaders from large energy companies in the hope of persuading them that the UK was an attractive venue for new nuclear investment.
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