Volkswagen AG will offer to buy back more than 500,000 diesel cars in the United States that used software to cheat on emission tests, according to reports Wednesday. The German automaker will also spend about $1 billion to compensate owners as part of the agreement.

Volkswagen admitted to using sophisticated software to cheat on emission tests for 11 million cars worldwide in September last year.

Following months of deliberation, the German automaker, the U.S. Federal authorities and private lawyers reached the deal, details of which are set to be announced Thursday at a court hearing, according to media reports.

The buyback would involve versions of the Jetta sedan, the Golf compact and the Audi A3 sold since 2009, which used a 2.0-liter diesel engine that exceeded legally permissible emission levels. Volkswagen is yet to announce remedial measures for 80,000 3.0-liter diesel vehicles also found to have exceeded U.S. pollution limits.

The agreement came just a day ahead of the April 21 deadline given to the company by U.S. District Judge Charles Breyer in March.

The "proposal may include a vehicle buy-back plan or a fix approved by the relevant regulators that allows the cars to remain on the road with certain modifications," Breyer said in March.

While Germany's Die Welt newspaper reported Wednesday that the deal to settle the case would see the company paying each affected customer $5,000, Reuters cited sources who said that no decision has been made on how individual compensation will be awarded. As part of the deal, owners are expected to have around two years to decide whether to sell back vehicles or get them repaired.