Ministers have described their backing for a new runway at Heathrow Airport as a "historic moment" for the UK.
The cabinet signed off the plans after they were approved by the government's economic sub-committee, which is chaired by Prime Minister Theresa May.
Transport Secretary Chris Grayling announced £2.6bn in compensation for residents and noise abatement measures.
Environmental groups oppose the plan, which Mr Grayling says will only happen if air quality commitments are met.
"The time for action is now," Mr Grayling told MPs, who will be asked to vote on the expansion plan by 11 July.
He insisted the decision was being taken in the national interest and would benefit the whole of the UK - with 15% of new landing slots at the airport "facilitating" regional connectivity.
He said the £14bn runway, which could be completed by 2026, would be funded entirely privately - but MPs warned that taxpayers would end up footing the bill for billions in road improvements and other upgrades and warned that the UK's carbon emission targets would be threatened by the increase in traffic around the enlarged airport.
A decision - finally?
The debate on expanding Heathrow has been going on for nearly 20 years.
The last Labour government backed the idea, and won a vote on it in 2009, but that plan was scrapped - and the idea of expansion put on hold for five years - by the Conservative-Lib Dem coalition formed after the 2010 election.
But the idea of expansion was resurrected and has been subsequently backed by the Conservatives.
Ministers approved a draft national airports policy statement in October but Parliament has yet to give its approval for detailed planning to begin.
Opponents have threatened a legal challenge while Foreign Secretary Boris Johnson, who is MP for Uxbridge and South Ruislip in west London, has vowed to "lie down in front of bulldozers" to prevent it.
The BBC's assistant political editor Norman Smith said ministers whose constituencies would be directly affected might be given a "get out of a jail card" - by being allowed to miss the vote or even vote against.
No 10 said Mrs May has written to ministers to say those with long-standing objections to a third runway will be permitted to restate their views at a local level, but not to campaign actively against the decision.
'So expensive': Why are critics opposed?
Campaigners argue that a new runway will breach the UK's legal limits on air pollution and increase noise pollution with an extra 700 planes a day.
It will result in huge disruption to residents of nearby villages, such as Longford, Harmondsworth and Sipson, with hundreds of homes likely to be knocked down.
Robert Barnstone, from the No 3rd Runway Coalition, told the BBC it was a "disappointing" day and the government was "failing people and failing the environment as well".
Former Transport Secretary Justine Greening, who backs expanding Gatwick instead, suggested the idea of Heathrow as a national hub airport was outdated and the focus should be on improving regional capacity.
"We are now moving to point-to-point travel," she told BBC Radio 4's Today. "Why should people who are living in Newcastle spend hours travelling down to London, then fly out somewhere else?
"There is nothing national about this national policy statement. It is just a runway in Heathrow."
And Tory MP Zac Goldsmith, who resigned his Richmond Park seat in 2016 over the issue and subsequently lost a by-election, said for many people "this doesn't just look like a blank cheque being given by this government to a foreign-owned multinational, it looks like a whole book of cheques signed by our constituents".
'Right for UK PLC'
Heathrow's owners, which include Spanish infrastructure firm Ferrovial, say the airport is virtually full and a new runway would increase its capacity from 85.5 million to 130 million passengers.
The expansion is estimated to create about 60,000 new jobs and generate about £70bn in total economic benefits by the 2050s.
Mr Grayling said it would provide a "vital legacy" for the British economy and said he had accepted 24 out of the 25 recommendations made by the Transport Select Committee to improve the plans.
Residents whose houses are knocked down will get compensation worth 125% of their value - as well as legal fees and stamp duty costs paid for - while £700m would be available to fund noise insulation measures for those who decide to stay.
He said a ban on night flights was an "absolute requirement" and non-negotiable while he said landing charges paid by airlines must stay at current levels.
"This runway cannot be built if it does not meet air quality rules," he added.
Sir Howard Davies, whose 2015 review recommended a new runway as long as environmental and community impacts were addressed, said "significant" concessions had been made on reducing early morning flights and minimising the impact on residents on the proposed flight path.
The political battle - by Laura Kuenssberg, BBC political editor
Yes, the decades-long debate about airports in Britain is returning (it's never gone for long) just at a time when the government is embroiled in rows it will struggle to win. As one cabinet minister joked, "it's the gift that keeps on giving".
However, with only Boris Johnson having big doubts around the cabinet table, the real rumpus will be in the Parliamentary Tory Party.
Plenty of Tory MPs have long held objections to Heathrow and they will be made loudly on the backbenches in the weeks to come. The government doesn't have a majority and remember, it wants to get this plan through the Commons by the end of the month.
If they can, it will be a demonstration of "look, we are getting on with things, it's not just Brexit!"
There will be howls, and the process even after this likely vote is a very long one. But the government can expect to get the vote through. Even if Labour opposes it, which it may well do on environmental grounds, the party is also split on the merits of the project so might not all vote together.
Labour and the SNP save the day?
Labour has said expanded capacity is vital to the UK economy but its support is conditional on tests being met on capacity, climate change, noise and air quality, as well as the wider economic benefits.
But there is also a split in opinion when it comes to individual MPs, with shadow chancellor John McDonnell - whose Hayes and Harlington constituency could see homes demolished - says he is "implacably opposed".
Shadow Transport Secretary Andy McDonald said his party would "follow the evidence" and not simply rely on assurances from Mr Grayling: "If the correct balance is not found then the courts will rightly intervene," he said.
Leader Jeremy Corbyn said: "Yes, there is a demand for increased airport capacity across the south east, two of the south east airports are working somewhat under capacity, Stansted and Luton. Gatwick and Heathrow are working at pretty well max capacity, let's look at it in that context."
The SNP's Alan Brown said the new runway had the support of the Scottish government, most Scottish airports and Scottish firms who recognised the "business benefits".
But Lib Dem leader Sir Vince Cable said the plans were an "expensive folly" and his party's 12 MPs would work with others to "put an end to this project once and for all".
And The Green Party's MP Caroline Lucas said it was a "disastrous decision" which "flew in the face of common sense and climate science".
The carbon question
As one would expect, there have been contrasting reactions from business and environmental groups.
The Institute of Directors said the end of arguments over Heathrow's future was within "touching distance".
"While the new runway is being built, we also need to make better use of capacity at existing airports in the South East, and indeed the rest of the country," said its director general Stephen Martin.
But Friends of The Earth said a new runway was not compatible with building a low-carbon economy.
"Heathrow expansion would be bad news for our climate and will bring more noise, air pollution and misery to local residents," said the organisation's Jenny Bates.