For hundreds of thousands of Volkswagen diesel owners who’ve been waiting to get rid of their smoggy cars, the day has finally arrived.

A $14.7 billion settlement with U.S. regulators over VW’s diesel-emissions cheating won final approval from U.S. District Court Judge Charles Breyer. The decision paves the way for VW owners to get cash compensation, a buyback or simply have the car repaired, although a repair has not yet been approved.

Consumers Union, mobilization and policy arm of Consumer Reports, applauded the approval of the final settlement and urged the government to maintain oversight over VW throughout the process.

"Volkswagen needs to make consumers whole, and this work starts today,"  said Laura MacCleery, vice president of policy and mobilization for Consumers Union. "We’re pleased that consumers can choose which remedy works best for them and receive cash compensation regardless of their choice."

This sentiment was echoed by other groups championing consumer protections. "There’s a sense from many consumers that they just want this done," said Dave Cooke, vehicles analyst at the Union of Concerned Scientists. "Now people can actually begin the process."

Once owners get their application processed by VW, they will be able to schedule a buyback appointment within 90 days, the German automaker said. Leaseholders will be able to schedule an appointment in 45 days.

There are already 336,000 consumers registered to receive settlement benefits, according to a hearing Breyer held last week—a little more than two-thirds of the estimated 475,000 affected owners. About 3,200 VW owners have opted out of the deal, preserving their rights to mount their own separate lawsuits.

VW called the judge’s approval "an important milestone in our journey to making things right in the United States."

"Volkswagen is committed to ensuring that the program is now carried out as seamlessly as possible for our affected customers and has devoted significant resources and personnel to making their experience a positive one," said Hinrich Woebcken, president and CEO of Volkswagen Group of America, Inc.

This deal also is exclusive to owners with 2.0-liter engines. About 85,000 owners of larger cars and SUVs with six-cylinder, 3.0-liter engines are waiting for their own settlement and government-approved fix.

The other elements of the settlement that can now get under way are a $2.7 billion program to clean the air through locally administered smog-control grants and a $2 billion investment VW has promised for electric-car infrastructure and consumer education.

The government agencies that negotiated with VW—the U.S. Justice Department, the Environmental Protection Agency, the Federal Trade Commission, and the California Air Resources Board (CARB)—promised consumers would get generous compensation for the diminished value of their cars, which can emit up to 40 times the permitted amount of smog-forming nitrogen oxides.

VW owners will have the option of selling their cars back to the company or keeping them and getting a free, government-approved repair. Either way, they’ll get cash payments ranging from $5,100 to $10,000. Making the decision to sell or fix won't be easy until more is known about the repair, how well it works, and how much it affects performance and fuel economy—which Consumer Reports will test. VW’s fix still hasn’t been approved by EPA and CARB.

The settlement creates a strong incentive for consumers to have their cars bought back, said Cooke of the Union of Concerned Scientists. If you’re a VW owner who’s already tired from having to wait more than a year to get to this point, you’ll have more months to wait to evaluate the potential repair. No one knows at this point how the recall will affect vehicle performance, and the market for the repaired cars isn’t expected to be great, Cooke said.

The EPA has been having a technical discussion with VW for months about how a fix will work, agency spokesman Nick Conger said. Now that the judge has approved the settlement, the next step will be for VW to formally submit the repair for review. The agreement gives EPA and CARB 45 days to evaluate the proposal, and the regulators are going to try to stick to that timetable, Conger said.