British Prime Minister Theresa May approved the decision at a Cabinet meeting after months of uncertainty over whether it would be Heathrow that would be chosen for expansion or Gatwick would get a second runway instead.
A public consultation will now be held on the impact of a third runway at the west London air traffic hub before the final decision is put to MPs for a vote in the House of Commons next year, with any new runway operational only by around 2025.
"Airport expansion is vital for the economic future of the whole of the UK and today also provides certainty to Londoners. Businesses will know that we are building the infrastructure they need to access global markets," May said.
"Ordinary, working people will know that my Government backs jobs and growth. We want the benefits of a new runway as quickly as possible, but we will also make sure London and taxpayers get a good deal," she added.
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Foreign secretary Boris Johnson and education secretary Justine Greening are among those firmly against the decision and Conservative party MP Zac Goldsmith had announced he would step down from the party if the government was to choose a third runway at Heathrow.
London Mayor Sadiq Khan said: "This is the wrong decision for London and the whole of Britain. The government are running roughshod over Londoners' views.
"I will continue to challenge this decision and I am exploring how I can best be involved in any legal process over the coming months."
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One of the leading Indian-origin Labour MPs, Virendra Sharma, whose constituency of Ealing, Southall, in west London is directly affected, has abandoned his original reservations for the plan.
"I've changed my mind on Heathrow expansion for the simple reason that Heathrow have engaged, listened and changed their plans.
"Now that Heathrow has accepted the Airports Commission conditions, West London can say 'yes' to the jobs, apprenticeships and investment that expansion will bring," Sharma said in a statement on Tuesday.
Last week, May moved to side-step potential Cabinet resignations over the issue by giving ministers freedom to speak out against the decision.
Downing Street said any ministers wanting to voice their opposition to the plans would have to seek permission from the Prime Minister in advance.
The government confirmed the scheme would be taken forward in the form of a draft national policy statement, which will be consulted on in the new year.
Construction of a new runway is not likely to begin until 2020 or 2021, according to the UK's Airports Commission.
Business groups have overwhelmingly welcomed today's decision.
"I am relieved that the decision has finally been made and firmly believe it is the right one. The constant dithering over a decision in past years has risked damaging British business but now we finally have the chance to act to future-proof the UK economy," said the London Chamber of Commerce and Industry.