Ministers approved the decision at a cabinet committee meeting on Tuesday, with construction of a third runway at Heathrow, rather than an extension, thought to be preferred.
However, Downing Street has yet to officially confirm the decision.
Transport Secretary Chris Grayling will make a statement to the House of Commons about 1pm on Tuesday.
But the decision faces a long consultation before it becomes final.
The manner in which the expansion would be carried out, a new runway or an extension to an existing one, has not been divulged.
A study last year, led by Sir Howard Davies, recommended a third runway at Heathrow but other options included a new runway at Gatwick or extending one of Heathrow's existing runways.
Last week Prime Minister Theresa May moved to head off possible Cabinet resignations by giving ministers freedom to speak out against the decision. Foreign Secretary Boris Johnson and Education
Secretary Justine Greening have been vocal critics of Heathrow expansion.
Downing Street said any ministers wanting to voice their opposition to the plans would have to seek permission from the prime minister in advance.
Ms Greening is expected to give her reaction to the decision in a message to her constituents in Putney, south-west London, a source said.
Mr Johnson will also make a statement if the government does favour expansion at Heathrow, it is understood.
A public consultation will now be held on the effects of airport expansion before the government makes a final decision as part of a National Policy Statement on Aviation.
MPs will then vote on that decision in the winter of 2017-18. It is unlikely that any new runway capacity would be operational before 2025.
Construction is not likely to begin until 2020 or 2021, the Airports Commission has said.
A final decision on which London airport to expand has been years in the making.
In 2009, former prime minister David Cameron pledged that there would be no new runway at Heathrow.