It means the competing plan for a shorter runway, as proposed by hotel tycoon Surinder Arora, has been rejected.
Heathrow says the project will be 100% privately financed, through higher airline costs, and no taxpayer money will be used to build the runway or the associated infrastructure.
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But it will require re-routing the M25 motorway – one of the busiest in the country and the demolition of nearby villages.
The proposal is still subject to the planning process, including consultation and parliamentary scrutiny.
The full length of the runway is not known, as the layout and associated infrastructure implications will continue to be considered by the Department for Transport.
The department added the selection of Heathrow’s scheme does not represent a final decision on a third runway or its design.
Heathrow plans to spend £33bn on the third runway and £15bn to upgrade the existing airport.
When could it be built?
The government hopes a planning decision will be made by 2029, with the third runway being built by 2035.
But Ryanair boss Michael O’Leary, who has consistently refused to use Heathrow on operational and cost grounds, has claimed the chance of it being built is “slim”, but it could be 2050 even if it does get built.
Ms Alexander said: “Today is another important step to enable a third runway… setting the direction for the remainder of our work to get the policy framework in place for airport expansion. This will allow a decision on a third runway plan this parliament which meets our key tests including on the environment and economic growth.
“We’re acting swiftly and decisively to get this project off the ground so we can realise its transformational potential for passengers, businesses, and our economy sooner.”
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