SAN FRANCISCO (AP) — A federal judge in San Francisco has approved a $15 billion court settlement of most claims against Volkswagen for its emissions-cheating scandal.

U.S. District Judge Charles Breyer signed the order Tuesday approving the largest auto-scandal settlement in the nation's history.

About 475,000 owners of VWs and Audis with 2-liter four-cylinder diesel engines now will be able to seek buybacks of their vehicles starting next Tuesday.

Most of the owners are expected to sell their cars back to VW after the company acknowledged cheating on emissions testing and putting dirty cars on the road. In addition to having their cars bought back, owners can each get cash payments of $5,100 to $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 $324 million in fees and $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.

The order says that 336,612 owners of 2-liter diesels have registered for the settlement and 3,298 have opted out.