At a cost of £33 billion, the development will enable more long-haul flights, but will also mean moving a section of the M25 motorway.
The plans will now centre on building a 2.2-mile-long runway north-west of the airport.
Transport secretary Heidi Alexander rejected a proposal by the Arora Group for a 1.7-mile runway costing £23 billion that would accommodate mainly short-haul flights in favour of the full fat option put forward by the airport itself.
Does this mean planning permission has been given?
No. The government has just given its formal backing to the scheme favoured by Heathrow Airport Limited (HAL) and rejected the Arora scheme.