Spanish police detained the pair in Barcelona in 2014 along with two Pakistani men, who have already been extradited, as part of a joint operation - dubbed Operation Yoga - with the U.S. Drug Enforcement Administration (DEA) to bust a smuggling ring based in the Catalonia region.
The group had offered the Russian-built Igla missiles to foreign paramilitary groups. The police could not immediately confirm when the pair were extradited.
The attorney's office in New York has charged them with drug and arms trafficking, and with financing terrorist organisations, the statement said. They face up to 30 years in prison.