A federal judge on Tuesday authorized a nearly $15 billion U.S. settlement over the Volkswagen Group emissions scandal, setting into motion a massive vehicle buyback program and green-lighting environmental remediation efforts.

Judge Charles Breyer of the U.S. District Court in San Francisco approved the sweeping agreement between consumers, the U.S. government, California regulators and the German automaker in a written ruling a week after signaling he was likely to sign off.

He said the agreement, widely considered one of the largest consumer settlements in U.S. history, is "fair, reasonable and adequate."

The settlement comes about a year after Volkswagen admitted that it rigged 11 million vehicles worldwide with software to dodge emissions standards.

The company is still facing criminal investigations by the U.S. Justice Department and German prosecutors. The U.S. probe could lead to additional financial penalties and criminal indictments.

About 475,000 Volkswagen owners in the U.S. can choose between a buyback or a free fix and compensation, if a repair becomes available. VW will begin administering the settlement immediately, having already devoted several hundred employees to handling the process.

"The priority was to get the polluting cars off the road as soon as possible. The settlement does that," Breyer said in his ruling, adding that even "under heightened scrutiny" the deal is laudable.

Buybacks range in value from $12,475 to $44,176, including restitution payments, and varying based on mileage. People who opt for a fix approved by the Environmental Protection Agency will receive payouts ranging from $5,100 to $9,852, depending on the book value of their car.

Volkswagen will also pay $2.7 billion for environmental mitigation and another $2 billion for clean-emissions infrastructure.

Approval marks an "important milestone in our journey to making things right in the United States, and we appreciate the efforts of all parties involved in this process," VW U.S. CEO Hinrich J. Woebcken said in a statement. "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."

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Judge 'inclined' to approve Volkswagen settlement

The company has also agreed to a $1.2 billion settlement with dealers over the same matter.

Meanwhile, VW is negotiating a separate settlement with more than 80,000 owners of 3-liter diesel vehicles fitted with similar software. Breyer will hold a hearing Nov. 3 to get updates on those talks.

More than 336,000 of the eligible VW 2-liter owners have already registered for the settlement, though they could back out if VW can't come up with a fix by Oct. 30, 2017. The company has yet to receive approval from the Environmental Protection Agency, and if it fails to do so, everyone will be offered the buyback option.

VW plaintiffs attorney Elizabeth Cabraser told Judge Breyer last week that the deal "set a land speed record — probably an air speed record as well."

Fewer than 1% of eligible VW owners opted out of the deal before September deadline. People who did not respond are automatically considered to have taken the offer.

About two dozen VW owners objected to the deal during an Oct. 18 hearing. Most of the objections boiled down to complaints over the amount of the payout, while some critics also lambasted the automaker's "clean diesel" advertising and purposeful environmental pollution.

But Breyer rejected all of those arguments in his ruling. The assertion that compensation should not be pegged to a vehicle's mileage ignores the fact that people "who frequently drove their vehicles undeniably got more use out of them," he said.

"The number of objections is small, and their substance does not call into doubt the settlement’s fairness," he ruled.

Eligible owners include 2-liter diesel versions of the 2013 through 2015 VW Beetle, 2010 through 2015 VW Golf, 2009 through 2015 VW Jetta, 2012 through 2015 VW Passat and 2010 through 2013 and 2015 Audi A3. They can visit VWCourtSettlement.com for more information.