Successive governments have dithered over whether to expand the site to the west of London, with politicians and the legal system caught between the need to build more capacity and concerns around the impact on pollution and carbon emissions.
Reeves said the case for a third runway at Heathrow, one of the world's busiest hubs, was stronger than ever and she wanted to see permission being granted by the end of this parliament, which will end in 2029.
The head of Heathrow, Thomas Woldbye, said a third runway could be operational by 2035.
"We cannot duck the decision (on Heathrow) any longer," Reeves said in a speech about economic growth. "I have always been clear that a third runway at Heathrow would unlock further growth, boost investment, increase exports and make the UK more open and more connected."
She said that "persistent delays" around a decision have cast doubt among international investors about Britain's "seriousness towards improving our economic prospects".
Even with the government's support, the plan - the country's most controversial infrastructure project - has numerous hurdles to overcome before construction can start, including how it would be financed and how it would navigate legal challenges.
French private equity group Ardian, Heathrow's biggest shareholder with a 23% stake, told the Financial Times in November that it would support management if it wanted to build a new runway.
Reeves's support puts the ball in Heathrow's court to submit a planning application.
Heathrow's most recent statement is that it is considering options "in line with strict tests on carbon, noise and air quality." It would also have to agree a funding model with investors and airlines.
Heathrow Airport is operating at 99% capacity and risks being overtaken in Europe. Its two runways compare with four each in Paris' Charles de Gaulle and Frankfurt Airport, and six at Amsterdam's Schiphol.
