The Abernedd Combined Cycle Gas Turbine Plant will be built at the Baglan Bay Energy Park, on the former site of a chemicals facility next to an existing gas-fired power station.
At peak construction the huge power plant is expected to create 900 jobs.
The 870MW station will be built in two distinct stages over five years with each project phase resulting in 435MW capacity being connected to the National Grid.
The government also gave the power company consent to retrofit its coal-plant in Fiddler’s Ferry in Warrington, north-west England, with a selective catalytic reduction plant to reduce emissions of nitrogen oxides.
Hendry said: “This new power station will bring jobs and industry back to this disused site and will provide a boost to the nation’s energy security.
“Gas is the cleanest and most reliable fossil fuel and it will continue to be a central part in the country’s energy mix during the transition to a low carbon economy.
“Long-term there is also a major opportunity for gas power stations like this to be fitted with abatement technology. This station will be built carbon capture ready, which means that eventually CO2 produced by the plant could be captured and transported for storage offshore.”