Saint-Jacques has spent years training for the six-month mission, which was originally scheduled for December 20 but was moved up after the aborted Soyuz launch.
Russian Federation said last month the launch of the Soyuz rocket failed because of a sensor that was damaged during assembly at the Baikonur cosmodrome.
The three-person crew's mission was originally scheduled for later this month, but officials brought it forward to avoid the ISS being left unmanned when its current crew return to earth.
A few minutes after their rocket lifted off from the Baikonur Cosmodrome, Russian space agency Roscomos announced that the capsule was "successfully launched into orbit".
I'm grateful to Director General Dmitry Rogozin and the entire @NASA and @roscosmos teams for their dedication to making this launch a success.
It was the first manned launch for the Soviet-era Soyuz since Oct 11, when a rocket carrying Russia's Aleksey Ovchinin and U.S. astronaut Nick Hague failed just minutes after blast-off, forcing the pair to make an emergency landing.
The Soyuz-FG rocket booster with Soyuz MS-11 space ship blasts off at the Russian leased Baikonur cosmodrome Kazakhstan on Monday
This is the first launch of manned spacecraft after the accident the carrier rocket "Soyuz-FG" with manned spacecraft "Soyuz MS-10", which was wrecked soon after launch from the Baikonur cosmodrome on October 11. She offered Saint-Jacques a "Bravo, bravo, bravo" and told the space station crew they were an inspiration for humanity.
"Risk is part of our profession", the 54-year-old said.
Astronauts Serena Aunon-Chancellor, Russian Sergei Prokopyev and German Alexander Gerst are at the space station waiting for their arrival.
But the rocket launch on Monday went smoothly.
After launching at 11.31am GMT the three are set to dock at the International Space Station at exactly 5.36pm GMT.
The Soyuz spacecraft is now the only vehicle that can ferry crews to the space station, but Russian Federation stands to lose that monopoly in the coming years with the arrival of SpaceX's Dragon and Boeing's Starliner crew capsules.
The last Canadian astronaut to visit the space station was Chris Hadfield, who was on a five-month mission that ended in May 2013.
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