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.
Greenpeace UK director John Sauven said:
Hinkley C fails every test - economic, consumer, and environmental.
It will lock a generation of consumers into higher energy bills via a strike price that's nearly double the current price of electricity, and it will distort energy policy by displacing newer, cleaner, technologies that are dropping dramatically in price.
With companies like Dong Energy now saying the price of offshore wind will drop so much it will be on par with nuclear by the 2020s, there is little rationale for allowing Hinkley C to proceed.
Giving it the green light when there is no credible plan for dealing with the waste is also unacceptable. David Cameron has said himself that, until the waste issue is sorted, no new investment is possible.
This is yet another Government U-turn which is creating uncertainty for investment in both energy efficiency and renewable energy, which, despite recent headlines, remain the best long-term solution for the consumer, energy security and tackling climate change.
John Cridland, CBI director-general, welcomed the Hinkley nuclear deal as a "fundamental feature of our future energy landscape."
This is a landmark deal which will help us meet our future energy challenges, while boosting jobs and growth.
New nuclear plants must be a fundamental feature of our future energy landscape, and Hinkley Point C is the starter gun to securing the investment we need.
Amid understandable public concern about rising bills, it's important to remember this investment will help mitigate the impact of increasing costs.
The fact is whatever we do, energy prices are going to have to go up to replace ageing infrastructure and meet climate change targets - unless we build new nuclear as part of a diverse energy mix.
"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."
"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."
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".
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."
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."
The Chancellor George Osborne will agree a deal this week that will see a Chinese firm become one of the main players in the building of a new nuclear power plant for Hinkley Point. It's a move that is welcomed by businesses in the area that will benefit.
Bob Constantine reports.