Donald Pratt with the Hassan Diab Support Committee confirms Diab left Canada around 5:30 a.m. Friday.
The Supreme Court said Thursday it would not hear Diab's appeal of the extradition order.
Pratt says Diab was not given a chance to say goodbye to his wife and young daughter — which Pratt called cruel.
French authorities suspect Diab, 60, was involved in the anti-Semitic bombing 34 years ago that killed four people and injured dozens of others — an accusation he denies.
In a statement released after the top court's decision, Diab described life since his arrest six years ago as a Kafkaesque nightmare and promised to never stop battling "the false allegations" levelled against him.
In keeping with standard practice, the Supreme Court gave no reason for its decision.
At this point, Diab is presumed to be innocent, the French Embassy in Ottawa has said. In France, he will be heard by an investigating judge in an open judicial inquiry regarding the attack, according to an embassy spokesman.