Heidi Alexander, transport secretary, approved the scheme with conditions on noise abatement and public transport provision.
Gatwick Airport said the project is privately financed, requiring no taxpayer money, and is shovel-ready.
The proposed plans involves shifting the airport’s emergency northern runway sideways by 12m and upgrading it for regular short-haul use.
This change will allow simultaneous operations on both runways while ensuring compliance with international safety standards.
Other aspects of the proposal include new buildings and extensions at both North and South Terminals.
Plans also include improvements to surrounding highways, including a new flyover across the South Terminal roundabout and an enlarged North Terminal Roundabout.
Up to 3,200 workers will be on site at peak construction.
Chancellor of the Exchequer, Rachel Reeves, said: “This Government promised to kickstart the economy – and we are.
“A second runway at Gatwick means thousands of more jobs and billions more in investment for the economy.
“We are backing the builders, not the blockers.”