Ministers have agreed £92.50 per megawatt hour that will be paid for electricity produced at the £14 billion Hinkley Point C power plant when it comes into operation in 2023, around double the current market rate.
The so-called 'strike price' could fall by £3 if another mooted development at Sizewell goes ahead, allowing for efficiencies in development and testing.
Energy Secretary Ed Davey has insisted that consumers will benefit in the long term, saving an average £77 on their bills a year by 2030 thanks to the new nuclear programme.
Under the deal with French-owned energy company EDF, he said that the construction risks will be borne by the companies involved and the Government would not be on the hook for any overspends. However, if costs fell, the taxpayer would share in the savings.
He added that all decommissioning and waste management costs were included in the deal.
But the consumer group Which? said the deal should include a clause which would trigger a refund to consumers if it turns out that the Government has overpaid.
Which? executive director Richard Lloyd said: "Rising energy bills are one of the top concerns for cash-strapped consumers, so everyone will want to be assured that the price the Government has agreed for new nuclear power is fair.
"The Hinkley deal commits billions of pounds of billpayers' money but it has been done without transparent, independent scrutiny.
"If it emerges that the Government has overpaid, we believe there should be a mechanism to refund consumers instead of a windfall to the suppliers.
"We can't afford to continue with a situation where suppliers and ministers blame each other for energy price rises.
"We now need an independent expert review, that reports to Parliament, of all energy policy costs, with an assessment of whether consumers are getting value for money and where savings can be made.
"The National Audit Office should also be responsible for ongoing reviews so that ministers' decisions are held to account and consumers can have more confidence that their money is being spent wisely."
Jonathan Isaby, political director of the TaxPayers' Alliance, said: "Subsidies to guarantee investment in nuclear power will be paid for by households through higher energy bills, at a time when throwing money at uneconomic forms of renewable energy has already pushed bills to breaking point.
"The Treasury's financial guarantee creates the danger of taxpayers bailing out French state-owned EDF if something goes wrong with the deal.
"Ministers should instead focus on more affordable forms of power generation available today, rather than guaranteeing profits for energy firms and leaving families to pay the price."
But Mr Davey insisted the new nuclear power station would be "really good value" for money.
He added that investing in schemes such as Hinkley C was essential to keep the "lights on" in Britain in the future as two thirds of electricity generating capacity was due to go "off line" over the next 15 years.
He said failing to build nuclear power stations would leave the consumer even more vulnerable to rising gas prices which would push up people's bills in the future.
"It is going to be really good value for money, because by the time you get to 2023 when it starts generating, in 10 years' time, we are going to live in a very different world for electricity and energy generally," he told ITV Daybreak.
"We calculate that by the end of the next decade, by 2030, this will actually be saving consumers money. We think the average consumer will be saving £77 a year on their bill thanks to the new nuclear programme that we are putting forward.
"So this is good value for money, we are getting a good deal for Britain and Britain's consumers and Britain's industry and I think it is going to restart Britain's nuclear industry."
Asked about energy companies that have already put their prices up, and if he would scrap the "green tax", Mr Davey said: "Just 4% on the bill is for renewables and for feed-in tariffs. The biggest rise on people's bills has been gas prices, wholesale gas prices have gone up by 50% in the last five years.
"The danger is that if we don't do things like replace our nuclear power stations, we will be ever more vulnerable to rising gas prices which will really push up people's bills in the future."