Piratheepan Nadarajah, from Brampton, Ont., admitted to a conspiracy to acquire anti-aircraft missiles and attempting to provide material support to a foreign terrorist organization.
Online court records, updated Wednesday, show that Nadarajah pleaded guilty last week in New York to the two counts.
His sentencing is scheduled for Jan. 31, 2014.
Prosecutors alleged Nadarajah and co-conspirators negotiated with an undercover FBI agent to buy and export $1 million of high-powered weapons and military equipment for the Tamil Tigers.
Nadarajah was extradited last year alongside Suresh Sriskandarajah, who pleaded guilty in July to conspiring to provide material support to the Tamil Tigers.
Prosecutors want Sriskandarajah, known as "Waterloo Suresh," to serve the maximum sentence of 15 years, while he is arguing for time served.
Sriskandarajah is due to be sentenced on Oct. 28.
The two men were arrested in Ontario in 2006 and freed on bail in 2009 during extradition proceedings. They appealed their extraditions all the way up to the Supreme Court of Canada and only after they lost those bids in December 2012 were they sent to the U.S.
Several co-conspirators have also been convicted of terrorism offences.
Last year an Ontario man was sentenced to time served for his role in the group. Ramanan Mylvaganam was a computer engineering student at the University of Waterloo and he pleaded guilty in the U.S. to conspiring to provide material support to a foreign terrorist organization.
The arrests followed a joint investigation by the FBI and the RCMP into an alleged plot to buy weapons, launder money through front charities and smuggle equipment to the rebel group.
The Tamil Tigers, notorious for suicide bombings and political assassinations in their fight for an independent homeland in Sri Lanka, were declared a terrorist organization by the U.S. in 1997 and by Canada in 2006.