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Energy Secretary Ed Davey told a news conference in London it was a "historic" day.
He said the UK was facing a "looming energy crisis" in the next decade thanks to years of neglect and under-investment.
Much of coal and nuclear-generated energy will stop in the coming years.
"We have known for years this is coming, but no-one was willing to take tough decisions."
Mr Davey stressed the project included plans to cover the costs of de-commissioning, with the operators required to pay into a fund from day one.
"We calculate that by the end of the next decade - by 2030 - this will actually be saving consumers money," Energy Secretary Ed Davey told ITV Daybreak.
"We think the average consumer will be saving £77 a year on their bill thanks to the new nuclear programme that we're putting forward."
Greenpeace UK director John Sauven said:
John Cridland, CBI director-general, welcomed the Hinkley nuclear deal as a "fundamental feature of our future energy landscape."
"If we're going to have cleaner energy, a more secure energy, it's not going to come without paying a price," Jeremy Nicholson, of the Energy Intensive Users Group, told Daybreak.
"The one thing we are guaranteed out of this," he went on, " we're going to get secure energy, and that's worth something."
But the Green Party's Baroness Jones said the Hinkley deal was "a disastrous decision".
"At the moment we don't know what to do with the nuclear waste and that means we are giving our children and our grandchildren a huge cost to pick up cleaning up after we've finished with this energy."
Energy Secretary Ed Davey has hailed a landmark deal to build Britain's first new nuclear plant in a generation.
But ministers are likely to face criticism over the report price that will be paid for electricity produced at the Somerset - around £90.00 per megawatt hour according to reports - which around double the current market rate.
"We think it would be good value if (the strike price) was a little higher," the Liberal Democrat Cabinet minister said.
"I was determined to get them below £90 so I could prove to everybody we had got a good deal...
"What has driven a tougher deal is the fact that I made clear we could walk away from the table. We had other nuclear options."
Prime Minister David Cameron said: "As part of our plan to help Britain succeed, after months of negotiation, today we have a deal for the first nuclear power station in a generation to be built in Britain.
"This deal means £16 billion of investment coming into the country and the creation of 25,000 jobs, which is brilliant news for the South West and for the country as a whole.
"As we compete in the tough global race, this underlines the confidence there is in Britain and makes clear that we are very much open for business.
"This also marks the next generation of nuclear power in Britain, which has an important part to play in contributing to our future energy needs and our longer term security of supply".
A deal has been struck with the Chinese which should see the development of Hinkley Point C nuclear power station near Bridgwater.
Chancellor George Osborne has confirmed the government will allow Chinese companies to take a stake, possibly leading to majority control, in British nuclear power plants, including Hinkley C.
Chief Executive of Somerset Chamber of Commerce, Rupert Cox, says it's good news.
Chancellor George Osborne has announced that the government is to give the go ahead to Chinese firms taking a stake in the development of the next generation of British nuclear power.
He made the announcement at Taishan nuclear power station in Southern China on the final day of his visit to China.
The Chancellor said: "Today is another demonstration of the next big step in the relationship between Britain and China - the world's oldest civil nuclear power and the world's fastest growing civil nuclear power.
"It is an important potential part of the government's plan for developing the next generation of nuclear power in Britain. It means the potential of more investment and jobs in Britain, and lower long-term energy costs for consumers."
Latest ITV News reports
David Cameron has insisted that plans for the UK's first nuclear power station in a generation at Hinkley was "not a deal at any price".
The Chancellor has given formal Government approval for Chinese state-run firms to buy into British nuclear power - should we be worried?