Ministers said they had imposed "significant new safeguards" for future foreign investment in critical infrastructure.
A statement said: "Following a comprehensive review of the Hinkley Point C project, and a revised agreement with EDF, the government has decided to proceed with the first new nuclear power station for a generation.
"However, ministers will impose a new legal framework for future foreign investment in Britain's critical infrastructure, which will include nuclear energy and apply after Hinkley."
Greg Clark, secretary of state for business, energy and industrial strategy, added: "Having thoroughly reviewed the proposal for Hinkley Point C, we will introduce a series of measures to enhance security and will ensure Hinkley cannot change hands without the government's agreement.
"Consequently, we have decided to proceed with the first new nuclear power station for a generation.
"Britain needs to upgrade its supplies of energy and we have always been clear that nuclear is an important part of ensuring our future low-carbon energy security."
Ministers said the agreement "in principle" with EDF means that the government will be able to prevent the sale of the French firm's controlling stake before completion of construction, without the prior notification and agreement of ministers.
The agreement will be confirmed in an exchange of letters between the government and EDF.
"Existing legal powers, and the new legal framework, will mean that the government is able to intervene in the sale of EDF's stake once Hinkley is operational," the government statement added.
"The new legal framework for future foreign investment in British critical infrastructure will mean that after Hinkley, the British Government will take a special share in all future nuclear new build projects.
"This will ensure that significant stakes cannot be sold without the government's knowledge or consent.
"The Office for Nuclear Regulation (ONR) will be directed to require notice from developers or operators of nuclear sites of any change of ownership or part-ownership.
"This will allow the government to advise or direct the ONR to take action to protect national security as a result of a change in ownership."
Unions welcomed the announcement, saying 25,000 jobs will be created by the project.
Unite national officer for energy Kevin Coyne said: "Our members are shovel ready and dead keen to start work on the country's first nuclear power station for a generation.
"It is excellent news that that the uncertainty caused by Theresa May's decision to put Hinkley Point 'on hold' has now been dispelled and that the government recognises the role of nuclear in a mixed energy economy.
"It means that the lights will remain on in the UK in the decades ahead and it heralds an economic renaissance for the West Country, with the accompanying creation of thousands of skilled jobs and the positive ripple effects to the supply chain across the UK.
"It is especially heartening that the new jobs will include 500 much-needed apprenticeships.
"This was the first big litmus test for big infrastructure projects, following June's EU referendum and shows that there is the appetite for giving the green light for such projects that the UK so desperately needs for its future economic prosperity."
A state-backed Chinese firm has a third stake in Hinkley and is pressing to build other new nuclear power stations in the UK including Bradwell in Essex.
Justin Bowden, GMB National Secretary for Energy, said: "Giving the thumbs-up to Hinkley is vital to fill the growing hole in the UK's energy supply needs.
"It will be a big relief for the 25,000 quality jobs which were put at risk by the latest delay, never mind the reputational damage inflicted on UK plc.
"GMB has always had reservations about linking Bradwell and Sizewell with the contract for Hinkley. The Government should never have allowed the country to be held over a Chinese barrel."
Claire Jakobsson, head of climate & environment policy at EEF ,the manufacturers' organisation, added: "This announcement provides some positive news for industry. With Hinkley C being such a major part of the government's energy strategy it is a relief to finally see the project given the green light after months of delays and uncertainty. It is encouraging to see investment in major UK infrastructure projects continuing to go ahead.
"However, this project will clearly require a vast amount of support and it remains to be seen whether this deal is able to offer value for money. If new nuclear is to continue to play a major role we must see significant reductions in strike prices for future projects."
Josh Hardie, CBI deputy director-general, said: "The final green light for Hinkley Point is good news for the UK's energy future as well as supporting jobs and growth across the South West and the country.
"New nuclear energy will play an important role in supporting a diverse, low-carbon and secure energy supply, so it's now time to push on with this key project.
"Investors are hungry for further signs from the government that the UK is open for business. Pressing ahead with major infrastructure decisions - such as giving clarity around the next Contracts for Difference auction and the post-2020 Levy Control Framework, and expanding runway capacity in the South East - would give a real boost to their confidence in the UK in the long run."
TUC general secretary Frances O'Grady said: "We are pleased ministers have ended the uncertainty over Hinkley Point. This project will create thousands of quality jobs and apprenticeships and bring much-needed investment to the South West.
"But the government must not stop here. It is time to get the shovels out for a third runway at Heathrow, high-speed rail and new affordable homes.
"Now is the time for the government to make the infrastructure investments our economy desperately needs."