The Airports Commission has backed a third Heathrow runway, saying it will add £147bn in economic growth and 70,000 jobs by 2050.
The report's release has revived intense debate over the runway's environmental impact.
Downing Street officials say they want to digest the report properly, without making "a snap judgement".
But London's Mayor, Boris Johnson, told the BBC that a new runway would have a "catastrophic" effect.
The idea of expanding Heathrow has always been surrounded by controversy because of its location in a heavily built-up area. Nearly 800 homes would have to be demolished to build the new runway.
Mr Johnson, who is also a Conservative MP, has consistently been a vocal opponent of plans for a new runway at Heathrow.
"It's not going to happen," he said.
He added that the "discomfort being endured" by Londoners on the hottest day of the year "would be nothing compared to the noise pollution that will be visited on hundreds of thousands, if not millions, of innocent people and the vehicular pollution as a result of a catastrophic decision to increase runway capacity in the west of the city".
Mr Johnson has proposed in the past a new airport in the Thames estuary.
Other high-profile politicians object to the expansion plans.
Richmond Park MP Zac Goldsmith, who is bidding to replace Mr Johnson as mayor of London, told the BBC he was strongly opposed to a potential new runway.
Pilots on board
The union that represents the UK's 9,000 pilots welcomed the report's recommendation of a new runway.
"Davies stresses the importance of the new runway for the UK economy and jobs and we need to make sure the extra capacity benefits Britain and is not simply exploited by our competitors," said Jim McAuslan, general secretary of the British Airline Pilots' Association (BALPA).
"Delivering the new airport capacity within the noise and environmental limits set by Davies will be a challenge and pilots stand ready to assist with the design to help minimise these impacts and ensure flight operations are safe," he also said.
Those noise and environmental issues have sparked an outcry amongst opponents.
Sir Howard Davies's report said that the new runway should come with severe restrictions to reduce the environmental and noise effects.
Night flights should be banned and the government should make a Parliamentary pledge not to build a fourth runway.
The report also recommends an aviation noise levy to fund insulation for homes and schools and says a legal commitment should be made on air quality.
The Commission admits that expanding Heathrow would mean many more people affected by noise compared to expanding Gatwick.
But it claims that quieter aircraft and home insulation would mean that overall noise levels would fall for people living near the airport by 2030.
The new runway would cost £17.6bn to deliver. Road and rail links around the airport would also have to be substantially changed, which could cost up to £5bn.
By contrast, a second runway at Gatwick would cost just over £7bn.
The Commission believes that both schemes would be funded by private finance.
Environmental groups, resident organisations and a number of prominent politicians have said they will campaign vigorously against any expansion of Heathrow.
"It would jeopardise the UK's climate targets, worsen air pollution in London, and open up a political can of worms for David Cameron," John Sauven, Greenpeace UK executive director, said.
"In the year of the Paris climate summit, what we should be really talking about is how to reduce emissions from aviation," he added.
In 2009, David Cameron pledged that there would be no new runway at Heathrow.
The government has said that it will give its official response to the Commission in the autumn and it is estimated that, if given the go-ahead, any new runway would take more than a decade to build.
"Heathrow offers the kind of long-haul connectivity - flights to emerging markets which are very important to the future of the British economy - and expanding it would allow Heathrow to offer more of those flights," Sir Howard told BBC Radio 4's Today programme.
He also said the airport would become "a better neighbour".
Sir Howard said that a second runway at Gatwick was a "credible" option but was less able to provide connections to long-haul destinations and would create lower levels of economic growth.
Heathrow welcomed the Commission's decision saying it would now work with government to "deliver expansion for all of Britain".
But Gatwick chief executive Stewart Wingate said the airport was "still very much in the race".
"The Commission's report makes clear that expansion at Gatwick is deliverable," he added.
'Clear and unanimous'
A third option for extending the present runways at Heathrow was rejected.
Sir Howard said that the recommendation for a new runway to the north of the present airport was "clear and unanimous".
It would also connect Britain to 40 new destinations.
"The best answer is to expand Heathrow's capacity through a new north-west runway," Sir Howard said.
"Heathrow is best placed to provide the type of capacity which is most urgently required: long haul destinations to new markets.
"It provides the greatest benefits for business passengers and the broader economy.
"Adding capacity at Heathrow also provides an opportunity to change the airport's relationship with its local communities.
"To make expansion possible the Commission recommends a comprehensive package of measures including a ban on night flights and a new noise levy to fund a far stronger and more generous set of compensation and mitigation schemes."
The chief executive of Heathrow stressed the economic benefits of a new runway.
"The Airports Commission has shown just how much it costs the UK economy to delay expansion of Heathrow," John Holland-Kaye told the BBC.
The British Chambers of Commerce (BCC) welcomed the report.
"Now that all the evidence is on the table, firms in every corner of the UK want to see an irreversible government commitment to a new runway at Heathrow by the end of 2015, with planning complete and diggers on the ground by the end of this parliament in 2020," said John Longworth, Director General of the BCC.