BAA has withdrawn its planning application for a third runway at London's Heathrow Airport following the election of the new government.
The airport operator's plans for a second runway at Stansted have also been pulled.
The move by BAA was a formality, since both the Conservative and Liberal Democrats had opposed new runways.
However, BAA will follow through with a pledge to buy up some homes on sites where the runways were set to be built.
"We recognise the importance of government policy in a matter as significant and controversial as runway capacity," said BAA's chief executive Colin Matthews.
However he said that Heathrow played "an important role for the UK and supports thousands of jobs".
"We continue to believe that new capacity would strengthen the UK's trading links with the global markets on which our economy and our competitiveness depend," Mr Matthews added.
BAA, supported by airlines and commerce in the capital, had argued that Heathrow needed extra capacity and without it London - and consequently the UK - would lose out to rival European cities as a place to visit and do business.
Both it, and the Stansted expansion, were envisaged in the government's 2003 aviation White Paper.
The Tories opposed the plans, preferring improved rail links to and from Heathrow, including a direct link to a new London-to-Scotland high-speed rail line.
Local residents and environmental campaigners had also protested against the expansions.
We asked you for your views on the scrapping of runway plans at Heathrow and Stansted. Here are a selection of your comments.
Great news for anyone living within 10 miles of Heathrow, like me. All day yesterday we had planes taking off and screaming over our house at low level so we couldn't relax properly in the garden. This never used to happen so I guess air traffic control are sharing out the take off routes so we all get a share of the noise.
Paul, Kempton Park
Marvellous news. There is very little of rural Essex left, and that was threatened with Stansted expansion and John Prescott's 300,000 new houses as well. Now there will be no new runway and the unelected undemocratic regional planning authority, which was pushing through the housing plans in spite of opposition by the local population and local authorities, is going to be scrapped as well! Time to break out the champagne!
Robert Leach, Halstead, Essex
This is predictable, I suppose. The question remains though, with night landings and take offs heavily restricted, where will Britain's hub airports get the capacity to cope with the increase in freight and passengers? Since this quite feasible plan has now been shelved, one alternative is to build a brand new airport on Green Belt land. Then listen to the wails from the eco-warriors.
Kevin Bennett, Newton Abbot
We need to reduce carbon emissions and because of the financial costs of runway and airport expansion in the south east of England these BAA plans never seemed in everyone's best interests. The expansion of regional airports are a much better option, but were opposed by BAA because they do not own them.
Malcolm Ewen, Furneux Pelham, Herts
This is such a complicated issue for the UK. The extra runways could greatly improve trading, keep up the high import and export facility of goods and most of all make it easier for commuters since Heathrow Airport is one of the world's busiest. On the other hand, they could cause many issues as whole villages will be wiped out, Green Belt would make way for concrete and more than this, Co2 emissions would be rising even further from London. To my knowledge, a flight takes off or lands at Heathrow every minute. I live about 20 minutes' drive from Heathrow and I can always see planes from my window. The noise doesn't disturb me - or maybe I'm immune to it by now. It's a very serious issue for Britain's transport systems.