The plant, the biggest of its kind to be built in the UK, will be on the site of the former coal-operated power station at Willington which closed during the 1990s.
The new power station, developed by RWE npower, will take about three years to build.
The company claimed the plant would create about 100 long-term jobs and bring £10m a year to the local economy.
The power station will be built with four CCGT generating units, each around 500MW in capacity, and four open cycle gas turbine (OCGT) generating units with a combined capacity of 400MW – bringing a total capacity of up to 2400 MW.
This brings the total new capacity consented by the Government since last May to 5.5GW.
Energy minister Charles Hendry said: “The Willington plant will play an important role in providing secure electricity supplies to millions of homes, as well as bringing jobs and investment to South Derbyshire.
“Gas plants like Willington will continue to be a central part in the country’s energy mix as we make move towards a low-carbon economy.”
He added: “There is a also a major opportunity in the long-term 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 emissions from the plant could be captured and transported for storage offshore.”