Volkswagen has gained approval from air regulators of the final modification plan for the remaining vehicles that contain software designed to defeat emissions tests, the California Air Resources Board has announced.

The U.S. Environmental Protection Agency has also signed off on the plan.

The final modification affects 3.0-liter Generation 1.2 diesels, and Volkswagen and Audi now need to submit their resale plans for the modified vehicles as the final step in the process that began in September of 2015, when researchers discovered the so-called defeat devices. Volkswagen eventually identified more than 500,000 VW, Audi, and Porsche vehicles in the U.S. as having the software, including more than 80,000 in California.

"This has been a long road," said Mary Nichols, the board's chair. "Mitigation of the harm from these vehicles will take years. But the process applied here is an excellent example of what can be accomplished when state and federal agencies actually work together."

In California, the vehicles released thousands of tons of excess nitrogen oxide emissions. Of the state's nearly 40 million residents, 10 million people live in areas designated by the EPA as extreme non-attainment areas with the highest air pollution. Nitrogen oxide can worsen the effects of cardiovascular disease, asthma, and other breathing problems.

Volkswagen has agreed to a financial settlement of $20 billion, which the company has mostly used to buy back affected vehicles and provide other customer compensation. California has received $423 million for mitigation of harm and VW has agreed to invest $800 million in zero emission vehicle technology in the state over the next decade. VW also paid California millions of dollars in civil penalties and compensation.

Here's a list of the vehicles in California with approved modifications:

• More than 10,000 2015, 2.0-liter, Generation 3, Beetle, Beetle convertible, Golf, Golf Sportwagen, Jetta, Passat, and Audi A3

• More than 6,000 2012-2014 2.0-liter, Generation 2, automatic transmission, Passat

• Approximately 47,000 2009-2014 2.0-liter, Generation 1, Jetta, Jetta Sportswagen, Golf, Beetle, Beetle convertible, and Audi 3

• Approximately 7,000 2013-2016, 3.0-liter, Generation 2, SUVs including VW Tourareg, Porsche Cayenne, and 2013-2015 Audi Q7

• Approximately 3,000 2009-2012 3.0-liter Generation 1, SUVs including VW Touareg, and Audi Q7

• Approximately 5,600 3.0-liter, Generation 2 passenger cars, including the Audi A6, A7, A8, A8L, and Q5.

Related: Volkswagen Storing 300,000 Diesels Around U.S.