Their Soyuz spacecraft entered a designated orbit just under nine minutes after the launch and is set to dock at the space outpost in about six hours after making four orbits of the Earth.
Saint-Jacques will be joined by Russian cosmonaut Oleg Kononenko and American astronaut Anne McClain on the mission, with liftoff scheduled for 6:31 a.m. ET Monday if all goes as planned. The Soyuz craft experienced a problem minutes after liftoff, en route to the International Space Station, but the capsule landed safely.
The launch was the first for the Soviet-era Soyuz since October 11, when a rocket carrying Russia's Aleksey Ovchinin and United States astronaut Nick Hague failed just minutes after blast-off, forcing the pair to make an emergency landing.
The incident on 11 October cast a spotlight on the safety of Russia's space programme, whose fleet have suffered a number of technical failures in recent years.
Reports say a Russian Orthodox priest blessed their rocket before its flight on Monday, as per tradition.
"Risk is part of our profession", the 54-year-old said at a press conference.
During their mission, members of the crew are scheduled to embark on a spacewalk to further probe a mysterious hole that caused a loss of air pressure on-board the ISS in August.
Anne McClain, a 39-year-old former military pilot, said the crew looked forward to going up.
Canadian astronaut David Saint-Jacques, 48, agreed that the Soyuz spacecraft was "incredibly safe".
McClain, Saint-Jacques and Kononenko will spend more than six months doing research and experiments in biology, Earth science, physical sciences and technology.
Russian Federation said last month the launch failed because of a sensor that was damaged during assembly at the Baikonur cosmodrome but insisted the spacecraft remained reliable.
The Soviet-designed Soyuz rocket is now the world's only lifeline to the ISS. CBC News Network will also broadcast the interactive special featuring Canadian astronaut Chris Hadfield.
Roscosmos, the Russian space agency, is now the only organisation transporting astronauts to the ISS after Nasa ended its space shuttle flights in 2011.
But the space agency's chief executive, former deputy prime minister Dimitry Rogozin, has been bullish about the project, according to Russian news agency Interfax.
He recently joked Russian Federation would send a mission to the Moon to "verify" whether or not NASA lunar landings ever took place.