Yesterday's decision brings to an end 60-year-old Hassan Diab's six-year legal battle to avoid what he said would be an unfair prosecution in France for a crime he insists he did not commit.
The Supreme Court of Canada issued its decision in a one-line statement, saying his appeal of a lower court ruling and the government's extradition order was "dismissed without costs."
Diab, who was taken into custody Wednesday pending the announcement, could now be flown to Paris at any time in the next 45 days. There he will be questioned by an investigating judge before criminal proceedings can begin.
The 1980 bombing on the narrow Copernic Street was the first fatal attack against the French Jewish community since the Nazi occupation in World War II.
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Explosives packed in the saddlebags of a parked motorcycle were detonated as worshippers were starting to exit the synagogue.
The blast killed three Frenchmen and a young Israeli woman. Forty were injured.
Guillaume Denoix de Saint-Marc, speaking for the victims' families, expressed "relief" that the case may now finally go to trial after 34 years.
Representative Council of French Jewish Institutions president Roger Cukierman told AFP the evidence was so compelling that "it would have been beyond understanding" if Canada had refused France's extradition request.
Dozens of people, including American activist Noam Chomsky and former Canadian solicitor general Warren Allmand, have pressed Ottawa to stop the extradition.
Diab's lawyer Donald Bayne maintained that the evidence "would never meet Canadian constitutional standards for a criminal trial."
"So it's a profoundly disappointing day in this legal journey," he said.
Diab was arrested at his home in an Ottawa suburb in November 2008 at the request of French authorities who alleged he was a member of the Popular Front of the Liberation of Palestine.