The payout has been described by lawyers as the largest car-related class-action settlement in US history.
The company has agreed to either buy back or repair the vehicles – although it has still to develop a way of fixing the problem. Owners will also receive payments of $5,100 to $10,000, (£5,100-£10,000) depending on the age of their vehicles.
Last year regulators in the US found that a number of VW cars were fitted with software capable of distorting emissions tests.
Some models could have been pumping out up to 40 times the legal limit of the pollutant nitrogen oxide, regulators disclosed.
The manufacturer subsequently announced that approximately 11 million cars were affected worldwide. However, consumer bodies have criticised the lack of government action in the UK to ensure British owners receive compensation.
Richard Lloyd, executive director of Which? said the government’s response had been “woefully slow” in comparison to the action taken by US authorities.
Gina McCarthy, administrator of the US Environmental Protection Agency, (EPA) said: “Using the power of the Clean Air Act, we’re getting VW’s polluting vehicles off the road and we’re reducing harmful pollution in our air – pollution that never should have been emitted in the first place. It should send a very clear message that when you break the laws designed to protect public health in this country, there are serious consequences.”
Elizabeth Cabraser, the lead attorney for consumers who sued the company, said that the judgment sent out a clear message to manufacturers in terms of their responsibilities to consumers.
“This historic agreement holds Volkswagen accountable for its betrayal of consumer trust and requires Volkswagen to repair the environmental damage it caused,” Ms Cabraser said.
The scandal emerged last September when US regulators revealed Volkswagen had fitted many cars with software to fool emissions tests and had put dirty vehicles on the road.
The company was caught after seven years by the International Council on Clean Transportation, which hired West Virginia University to test a VW in real roads conditions. The EPA has since changed its testing to include on-road tailpipe checks.