US District Judge Charles Breyer signed the order approving the largest auto-scandal settlement in the nation's history.
Volkswagen admitted last year that about 475,000 VWs and Audis with 2-liter four-cylinder diesel engines were programmed to cheat on emissions tests.
Under the settlement, owners of the affected cars have until September 1, 2018, to decide whether to have the car fixed or repurchased.
Volkswagen could start buying back the cars as early as next month if the owner submits a claim.
In addition to having their cars bought back, owners can each get cash payments of USD 5,100 to USD 10,000.
"The settlement is fair, reasonable and adequate," Breyer wrote in his order, posted Tuesday morning by the court.
VW will pay attorney fees and costs, including up to USD 324 million in fees and USD 8.5 million in out-of-pocket costs.
The settlement releases legal claims from most of the 2-liter VW owners, but it doesn't affect larger 3-liter six-cylinder diesels, which also cheated on tests. The settlement also doesn't end any claims against parts supplier Robert Bosch, which drew up the cheating software.
Breyer wrote that the priority was to get the cars off the road as soon as possible, and the settlement accomplishes that. The polluting cars emitted as much as 40 times the allowable limit for nitrogen oxide, a gas that can cause human respiratory problems.
The settlement calls for the German automaker to spend up to USD 10 billion to buy back or repair the affected cars. The company will buy back the cars at the National Automobile Dealers Association clean trade-in price before the cheating was made public on September 18, 2015.
But Volkswagen attorney Robert Giuffra encouraged Breyer to approve the deal, saying it was good for buyers and would help the company regain people's trust.
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