ScottishPower Generation estimates that the new power station will create up to 1,000 construction and demolition jobs.
The existing coal-fired power station on the site is due to end operations in December 2015, when it will be demolished
The development will be carbon capture ready and will be required to fit full carbon capture and storage technology once it is commercially and technically proven.
A separate application for a 17.5 km feeder gas pipeline from East Fortune has also been approved.
Energy Minister Fergus Ewing said: “Cockenzie power station is now over 40 years old.
“The new gas station will provide a far cleaner source of baseload electricity, with less than half the amount of carbon emissions, creating new jobs in East Lothian and new opportunities for existing Cockenzie staff in the process.
The 1,000 MW power station will consist of two combined cycle gas turbine units.
Scotland is expected needed a minimum of 2.5 GW extra generation by 2030 to support renewables targets.
This will be met by new build plants and upgrades to existing plants.
