The settlement filed in federal court calls for the German auto giant to either buy back or fix the cars that tricked pollution tests, and to pay each owner up to $10,000 in cash.
Under the agreement, Volkswagen has agreed to create a pool of $10 billion to compensate owners and a $2.7 billion environmental penalty.
The company will invest an additional $2.0 billion “to create infrastructure for and promote public awareness of zero emission vehicles,” the court filing showed.
The huge settlement, which must be approved by a federal judge in San Francisco who is overseeing the litigation, could affect some 480,000 owners of Volkswagens and Audis with 2.0-liter diesel engines.
Volkswagen admitted in September that it had installed software in the vehicles that tricked US emissions tests into showing the cars met environmental standards.
The device switched off after testing, enabling the vehicles to spew up to 40 times the permitted amounts of nitrogen oxides.
Volkswagen has set aside €16.2 billion ($17.9 billion) to cover costs from the scandal including the legal risks.
A settlement would not end Volkswagen's troubles in the United States, however.
VW also faces fines from US regulators potentially running to the tens of billions of dollars, and a criminal investigation over the scandal. It must address similar charges over its 3.0 liter diesel cars with emissions-cheating devices.
The auto giant is facing similar charges and litigation in Europe and elsewhere for the same issues.
Tuesday's settlement filed with Judge Charles Breyer would settle claims from the US government as well as a large number of plaintiffs including owners, lessees, and dealers.
Volkswagen agreed under the deal to buy back the emissions-cheating vehicles at their market prices before the scandal broke, at prices ranging from $12,475 for the Jetta Sedan to more than $44,000 for some Audi models.
The owners also have the option of letting Volkswagen modify the cars to meet US pollution standards.
In either case, the owners would also get a cash settlement ranging from $5,100 to $10,000 depending on the vehicle.