Transport Secretary Chris Grayling told the House of Commons the cabinet had agreed the controversial move, an action he described as “in the national interest”.
However, Mr Grayling admitted the decision was not “easy” and noted the “strength of feeling” among local residents in west London and under the airport’s flight path.
Critics of Heathrow expansion include a number of prominent Tory MPs as well as Foreign Secretary Boris Johnson, who has previously vowed to lie down “in front of those bulldozers and stop the building, stop the construction of that third runway”.
After Mr Grayling’s delivery of an Airports National Policy Statement, a vote on a third runway is now required in the House of Commons within 21 sitting days.
It was reported Mr Johnson will get round having to vote against the government by travelling abroad when the vote is held.
Mr Grayling revealed some dissent within cabinet at the decision – reported to have only come from Mr Johnson – but dodged a question on whether anti-expansion ministers would be able to navigate around collective responsibility on the issue.
Downing Street later revealed the prime minister has written to ministers saying they will be permitted to state long-standing views on Heathrow to local media.
A spokesman revealed Mr Johnson “restated his own position, which is a long-standing one” during a cabinet meeting on Tuesday morning.
Labour also face their own internal divisions on the issue, with shadow chancellor John McDonnell opposed to expansion, but leading trade unions supportive of a new runway at Heathrow.
Despite Tuesday’s announcement, Mr Grayling confessed “a new operational runway at Heathrow is still a number of years away” with the airport’s owners setting a target date of 2026.
But, the transport secretary stressed the estimated economic benefits of expanding the UK’s largest airport.
He said: “Heathrow is already full and the evidence shows the remaining London airports won’t be far behind.
“Despite being the busiest two-runway airport in the world, Heathrow’s capacity constraints mean it is falling behind its global competitors – impacting the UK’s economy and global trading opportunities.
“Expansion at Heathrow will bring real benefits across the country including a boost of up to £74bn to passengers and the wider economy, providing better connections to growing world markets, and increasing flights to more long haul destinations.
“Heathrow is a nationally significant freight hub, carrying more freight by value than all other UK airports combined.
“A third runway would enable it nearly to double its current freight capacity.”
Mr Grayling pledged £2.6bn for local communities in compensation, noise insulation and improvements to local amenities, which he said was 10 times bigger than under a previous bid for a third runway in 2009.
Prime Minister Theresa May, whose Maidenhead constituents live under the flight path, opposed those plans at the time, although criticisms published on her personal website at the time appear to have since been deleted.
Mr Grayling also told MPs the privately-financed expansion will secure “global connectivity, creating tens of thousands of local jobs and apprenticeships, and boosting our economy for future generations”.
Shadow transport secretary Andy McDonald kept coy on Labour’s stance, outlining his party’s four tests for airport expansion.
He said: “Expansion should only happen if it can effectively deliver on the capacity demands, if noise and air quality issues are fully addressed, if the UK’s climate change obligations are met in their entirety, and that growth across the country is supported.
“We owe it to future generations to get all of these factors absolutely right, but if the correct balance isn’t found then the law courts will quite rightly intervene.”
Mr McDonald also highlighted Mr Grayling’s difficulties amid ongoing rail chaos, asking why MPs should “accept what he says about the most significant of infrastructure projects”.
Telling Mr Grayling that MPs had lost confidence in him, Mr McDonald claimed he was only still in his role because “the prime minister is too weak to sack him”.
Mr McDonnell confirmed he remains “implacably opposed” to expansion at Heathrow, posting on Twitter: “I am even more convinced that this would be a costly, environmental and social disaster that will never be built.”
Labour leader Jeremy Corbyn has also previously voiced his opposition to a new runway, but faces a tricky balancing act after a number of his trade union allies joined business groups in praising the government’s decision and urged MPs to back Heathrow expansion.
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Liberal Democrat leader Sir Vince Cable called for a free vote on the issue, in order for MPs to “vote with their consciences on an issue that has negative economic consequences across many regions of the country”.
Prominent Tory backbenchers Justine Greening, the former education secretary, and Zac Goldsmith criticised the government’s decision.