The green light for the £18bn project in Somerset will now lead to thousands of jobs bring created during the building phase.
A so-called contract for difference was signed in London by Business Secretary Greg Clark, Jean-Bernard Levy, chairman of French energy giant EDF, and He Yu, chairman of Chinese firm CGN which has a third stake in the scheme.
French foreign minister Jean-Marc Ayrault and Chinese energy minister Nur Bekri were also in attendance at the event.
Clark said: "Signing the contract for difference for Hinkley Point C is a crucial moment in the UK's first new nuclear power station for a generation and follows new measures put in place by government to strengthen security and ownership.
"Britain needs to upgrade its supplies of energy, and we have always been clear that nuclear power stations like Hinkley play an important part in ensuring our future low-carbon energy security."
The Low Carbon Contracts Company will manage the contract on behalf of the government.
It provides a set price of £92.50 per megawatt hour of electricity provided by Hinkley Point C for 35 years once it begins generating.
Hinkley Point C will be the first new nuclear power station to be built in the UK in a generation.
It will produce 7GW of electricity for six million homes.
The government published documents detailing the contractual obligations it has entered into, including a so-called value for money assessment that allowed ministers to make the decision to proceed with the project.
Hinkley will provide 7% of Britain's electricity needs for 60 years.
UK-based businesses will benefit from more than 60% of the project and 26,000 jobs and apprenticeships will be created.
The board of EDF gave its final investment decision in July but the UK government said it wanted more time to study the details.
The government approved the project earlier this month and the signing ceremony completes the process.
Unions welcomed the development, saying thousands of skilled jobs will now be created, benefiting firms across the UK.