The package consists of a US$500 ($710) prepaid Visa card, a US$500 ($710) Volkswagen dealership card and three years of free roadside assistance.
While the prepaid credit card works at any location that accepts Visa cards, the dealership card can be only used at participating dealers affiliated with Volkswagen USA.
To see if they are eligible, Volkswagen owners need to check out www.vwdieselinfo.com and enter their car's VIN.
Owners and lessees that are entitled to these gifts will receive their goodwill package within four weeks of registering online. They will then need to show up at a Volkswagen dealership, with their car, ID, goodwill package and proof of ownership, to have the cards and roadside assistance service activated.
Registrations for the package must be received by the end of April 2016, and is only available to people who owned or leased an affected vehicle prior to the announcement of the deal. The Visa and dealership card are valid for one year after activation.
According to Volkswagen, the freebies are just the "first step toward restoring your invaluable trust".
At present only Volkswagen-branded vehicles sold in the USA with 2.0-litre EA189 TDI engine are eligible for the goodwill package. Automotive News reports that Audi USA is preparing a similar deal for its affected owners.
The company has admitted that around 482,000 Volkswagen and Audi vehicles were sold in the US with software designed specifically to cheat its way past emissions testing.
It's not known at this stage if Volkswagen in other regions around the world will offer similar deals to owners of similarly equipped cars.
Volkswagen also points out that today's goodwill package is not available to owners of vehicles fitted with a 3.0-litre V6 TDI. Last week, the United States Environmental Protection Agency claimed that some vehicles fitted with this engine also had emissions testing defeat devices installed.
Affected cars include the Volkswagen Touareg, Porsche Cayenne and a collection of Audi models. At the time Volkswagen denied the EPA's allegation, but according to the company's latest statement it "is currently investigating the allegations regarding 3.0L V-6 engines set forth by the Environmental Protection Agency and the California Air Resources Board on November 2 and is cooperating fully with the agencies".
Update I: A Volkswagen spokesperson has told Automotive News that in accepting the goodwill package, the owner or lessee doesn't indemnify Volkswagen against any legal claims that they choose to take part in.
Update II: The industry publication reports that there is a clause in the terms and conditions indemnifying the company from lawsuits related to the goodwill package.
According to company, "affected customers eligible for the Goodwill Package are not required to waive their rights or release their claims against VWGoA [Volkswagen Group of America] in order to receive the Package".