“This is a relief,” said Kevin Helmich, owner of a 2010 Audi A3, who plans to sell his car back to the company.

A sales executive at a wind-energy company in Ann Arbor, Mich., Mr. Helmich said he bought the car because he believed Volkswagen’s claims that its fuel-efficient diesels help reduce greenhouse gas emissions. He said it has not felt good driving the car for the last year, or knowing he was deceived by the company.

“While I really like the car, I don’t like being lied to,” he said.

Owners who wish to sell their cars back to Volkswagen can register on a website, VWCourtSettlement.com. Under the agreement approved by Judge Breyer, Volkswagen will pay the full market value for the vehicles from before the company admitted its cheating in September 2015, and up to $10,000 in compensation money on top of that.

The actual price depends on the model and how many miles the owners have driven their cars.

Mr. Helmich said his car, with 108,000 miles on the odometer, will be purchased for just over $21,000. He originally paid $37,650 for it. “It’s a reasonable deal,” he said. “I’m just waiting to hear when the car will be bought back.”

He’s already got a new environmentally friendly ride in mind: an all-electric, battery-powered Chevrolet Bolt, which General Motors has said can go 238 miles before needing to recharge.