SAN FRANCISCO — The owners of nearly half a million polluting Volkswagens in the U.S. will be given the option of selling them back to the company or getting them repaired at VW’s expense, under a deal announced by a federal judge Thursday

Senior U.S. District Judge Charles Breyer, who is overseeing a tangle of litigation over the VW emissions scandal, gave no details on how much car owners would be paid but said the tentative agreement between the automaker, the U.S. government and plaintiffs’ attorneys would include “substantial compensation.”

However, a person who was briefed on the matter said Wednesday Volkswagen would spend just more than $1 billion to compensate owners.

The judge also did not say how the vehicles would be repaired. He said the terms of the agreement were still being worked out and ordered all sides to keep them confidential during negotiations.

“I am extremely pleased to report that the parties have come up with a concrete plan by today’s date,” said Breyer, who had set Thursday as the deadline for an agreement.

The deal affects the owners of about 482,000 Volkswagens with 2-liter, four-cylinder diesel engines, most of them VW Jetta, Golf and Passat models dating to the 2009 model year.