Sayfildin Tahir Sharif is accused of murder and supporting a terrorist group that took part in suicide bombings in his native Iraq.
The Americans allege Sharif worked from Edmonton to help a Tunisian man enter Iraq in 2009 and detonate a truck filled with explosives at a military checkpoint, killing five U.S. soldiers.
Prosecutors contend that evidence from intercepted Internet and phone conversations shows that Sharif was directly involved in supporting Tunisian terrorists, who conducted the suicide bombing, by helping them make contact with other supporters as they made their way across the Middle East to Iraq.
The terror network is also accused of blowing up an Iraqi police station, killing seven Iraqi officers.
Sharif, who also goes by Faruq Khalil Muhammad Isa as well as another name, has been in custody in Edmonton since his arrest in January 2011.
Canada's justice minister granted extradition last summer after receiving assurances from the U.S. that Sharif wouldn't face the death penalty. Defence lawyers also received a letter from U.S. authorities promising the man wouldn't be held indefinitely in pre-trial detention.
Sharif was appealing the justice minister's decision as well as a judge's original ruling in 2012 that there was enough evidence to extradite Sharif on two charges.
Sharif is an ethnic Kurd who was born in Iraq but moved to Toronto as a refugee in 1993. Four years later, he became a Canadian citizen.
In 2011, he was arrested at an Edmonton apartment where he lived with his girlfriend and her children.
Defence lawyers had argued before the Appeal Court that RCMP didn't allow Sharif access to a lawyer or interpreter the day of his arrest, and transcripts of police interviews show he didn't understand what was going on.
They also said allegations against their client came from three people, including his brother, who were tortured by investigators in Iraq.
The Appeal Court ruled that none of the arguments merited keeping Sharif in Canada.