UK Transport Secretary Chris Grayling announced that the Heathrow expansion had been chosen as the preferred option ahead of a rival bid by Gatwick.
The Scottish government formally backed the Heathrow bid earlier this month.
It came after the airport made a list of commitments to Scotland, including creating up to 16,000 jobs and investing Â£200m in the country.
Heathrow also said it would help to develop new domestic routes to Scottish airports, and would investigate whether Prestwick Airport - which is owned by the Scottish government - could be used as a "logistics hub" for the new runway.
Responding to Mr Grayling's announcement, Scotland's economy secretary Keith Brown said he looked forward to the UK government "cracking on with this as soon as possible", while stressing that environmental and planning restraints needed to be taken into account.
Mr Brown said: "We announced our support for the third runway at Heathrow two weeks ago, so we are pleased that the UK government has the same view."
He predicted there would be "a number of benefits for people in Scotland" as a result of the decision, including "around Â£200m of spend for companies in Scotland, and the establishment of a hub airport in Scotland to support for Heathrow as its undergoing its change in infrastructure".
And he added: "Potentially we've seen the airports commission saying there could be around 16,000 jobs for Scotland, and obviously we want to see that followed through.
"Beyond that, increased connectedness between Scotland and the rest of the world will benefit our economy and our tourist industry."
AGS Airports, which owns Glasgow and Aberdeen airports, also welcomed the announcement, which it said would play an important role in supporting the Scottish economy.
But the operators of Edinburgh Airport said ahead of the decision that they believed Gatwick "offered the better deal for Scotland" and described the Heathrow plan as "undeliverable" and potentially "bad for passengers".
And both the Scottish Greens and Scottish Liberal Democrats have criticised the announcement.
The plan to build a new runway at Heathrow - which is expected to cost more than Â£17bn - now faces a long consultation before it becomes reality, with MPs not voting on the proposals until 2017 or 2018, and the new runway not being opened until 2025 at the earliest.
Several Conservative MPs oppose the proposals, including Foreign Secretary Boris Johnson, Education Secretary Justine Greening and former London Mayor candidate Zac Goldsmith, who has resigned as an MP in protest.
The opposition largely centres concerns about the noise and environmental impact of Heathrow expansion, with the decision expected to lead to further protests and legal challenges.
Some 783 homes will have to be demolished for the third runway, according to the Airports Commission, including the entire community of Longford and much of Harmondsworth.
The new runway will also mean several other residential areas will fall under the Heathrow flight path for the first time.
But most airlines and business groups are in favour of expanding Heathrow - Britain's busiest airport - as it offers more direct connections than Gatwick and handles more freight.
Heathrow is already operating at 98% capacity and Gatwick is expected to run out of space in the next few years, but the decision on how to increase air capacity in the south east of England had been hit by delays.
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.
As he confirmed Heathrow as the government's preferred option, Mr Grayling said: "A new runway at Heathrow will improve connectivity in the UK itself and crucially boost our connections with the rest of the world, supporting exports, trade and job opportunities.
"This isn't just a great deal for business, it's a great deal for passengers who will also benefit from access to more airlines, destinations and flights."
And the Secretary of State for Scotland, David Mundell, insisted a new Heathrow runway would provide a "major boost for the Scottish economy for decades to come" by providing better air links for business, with the promise of greater competition "pushing down on fares for everyone".
Business body the Scottish Chambers Commerce said it was pleased that a decision had been made, but called on the UK government to speed up the final process.
Chief executive Liz Cameron said: "London's major airports are continuing to operate at or near capacity and the longer it takes before work starts on expansion, the further behind our competitor nations we will fall in terms of connectivity.
"Now more than ever, Scotland's businesses need to be connected to the world, as we look to secure trading links the world over and encourage more of our businesses to export, particularly our small and medium sized businesses."
But Scottish Greens MSP John Finnie criticised the UK's government's decision and the Scottish government's support for it.
Mr Finnie said: "This will damage the UK's credibility on the global stage where there is firm agreement on the need to reduce climate emissions.
"What is perhaps a surprise is the Scottish government's support for today's decision, given that it does nothing to advance social justice. Wealthy frequent fliers will benefit, as they will from Scottish Ministers' desire to cut Air Passenger Duty."
The Scottish Liberal Democrats also criticised the Heathrow decision, arguing that any growth in capacity should be spread across the UK and not just focused in London.
The party's transport spokesman, Mike Rumbles, said: "The SNP have utterly failed to square their backing for Heathrow with their climate change commitments and ambition to reduce environmentally damaging short-haul flights."
The decision to build a third runway at Heathrow Airport will benefit Scotland, the Scottish government has said.