Although arrested several years ago, Mr Griffiths has spent the last three years in an Australian jail fighting extradition to America to face charges. The extradition was one of the first for an intellectual property crime.
"Whether committed with a gun or a keyboard - theft is theft," said US Attorney Chuck Rosenberg in a statement.
Sentenced to 51 months on a charge of "conspiracy to commit criminal copyright infringement", Mr Griffiths is likely only to serve a further 15 months in jail because of the time he has already spent incarcerated in Australia.
DrinkOrDie is thought to have been founded in Russia in 1993 and offered people cracked versions of programs from Microsoft, Adobe, Autodesk, Symantec, Novell and many others.
Under the banner of Operation Buccaneer, 70 raids were carried out to dismantle the group. Most raids took place in the US but law enforcement authorities in United Kingdom, Finland, Norway, Sweden and Australia also took part.
More than 30 people are known to have been jailed as a result of arrests made during the operation.