In a vote late on Monday, the House of Commons supported the plan by 415 to 119, giving the government a huge majority of 296.
Ministers were aided by the support of 119 Labour MPs voting in favour of the plan, with many of the party’s trade union backers in favour of a third runway.
Eight Tory MPs, including ex-ministers Justine Greening and Greg Hands, rebelled against the party’s three-line whip and voted against expansion.
And Labour leader Jeremy Corbyn, who gave his MPs a free vote on the issue, was joined by 93 of his colleagues in voting against a third runway.
The SNP abstained in protest at what they claimed was a failure by the government to provide guarantees the scheme will benefit Scotland.
Despite securing parliamentary backing for their plan, ministers still face a number of obstacles before construction can begin in west London.
Immediately after the vote result, Greenpeace vowed to join a cross-party group of London councils and the city’s mayor Sadiq Khan in a legal challenge.
Previous plans to expand Heathrow have foundered in the courts.
Monday’s proceedings were subject to a demonstration by a dozen protesters lying down in parliament’s central lobby while chanting “vote no, Heathrow”.
They later left voluntarily.
Greenpeace UK’s executive director John Sauven said: “This Heathrow flight has failed all safety checks, yet ministers have boarded it anyway and persuaded a majority of MPs to go along with them.
“But we can’t just look the other way while the whole dashboard flashes red with warning lights.
“The UK government won’t be able to tackle illegal levels of air pollution, never mind leaving a healthier environment to the next generation, if a new Heathrow runway is built.
“If ministers don’t want to uphold the laws protecting us from toxic fumes and climate change, we’re going to ask a court to do that.”
Foreign Secretary Boris Johnson, who famously vowed to lie down in front of bulldozers to prevent expansion of the airport, was visiting Afghanistan and so skipped the vote.
The trip, during which Mr Johnson met NATO and Afghanistan officials as well as British troops, allowed the cabinet minister to avoid having to resign from government in order to register his disapproval of expanding Heathrow.
A debate on the government’s Heathrow plan preceding Monday’s vote was dominated by jibes at his decision to make himself absent from the Commons.
Labour’s Mike Gapes quipped: “Apparently the foreign secretary couldn’t be with us today because he is in Afghanistan.
“He’s got his Khyber Pass, what a Carry On.”
Mr Hands, who quit as an international trade minister in order to vote against a third runway, sent a thinly veiled rebuke to Mr Johnson.
He told MPs: “This is not just for me a debate about Heathrow, important though that is, it’s also a debate about being true to your word and to your election pledges.”
Shouts of “Where’s Boris?” emerged as Mr Hands urged colleagues to join him in opposing the project.
As critics voiced concerns about the proposal’s environmental impact and its financing, Ms Greening claimed the saga of Heathrow’s third runway was “a story of broken promises, broken politics and broken economics”.
Labour’s shadow chancellor John McDonnell predicted the airport’s expansion would become an “iconic, totemic battleground of climate change which will attract protesters and campaigners from across Europe”.
“This issue will not go away,” he told MPs.
Liberal Democrat leader Sir Vince Cable claimed Heathrow is “an exceedingly dodgy company by any reckoning” as he questioned the airport’s owners competence in “managing the kind of risky project that is now envisioned”.
Transport Secretary Chris Grayling had earlier told MPs support for the new runway would set a “clear path to our future as a global nation in the post-Brexit world”.
He said: “This is a really important moment in the history of this House and the history of this country.”
After the result, Heathrow’s chief executive John Holland-Kaye said: “Parliament has ended 50 years of debate by deciding that Heathrow expansion will go ahead.
“This vote will see us deliver more jobs, create a lasting legacy of skills for future generations and guarantee expansion is delivered responsibly.
“We are grateful that MPs have made the right choice for Britain and today we start work to create the best connected hub airport in the world.”
If Heathrow is granted development consent following a planned public consultation, construction would begin in 2021 ahead of the third runway opening in 2026.