Of the trio set to reach the ISS six hours after blast-off, both Saint-Jacques and McClain are flying for the first time.
This was the first time people rode on one of the Russian rockets since October 11, when two and a half minutes after takeoff, one of the Soyuz MS-10's four boosters broke off, sending the aircraft spinning out of control.
Last month Russian Federation said the October launch had failed because of a sensor that was damaged during assembly at the Baikonur cosmodrome but insisted the spacecraft remained reliable.
The launch was closely scrutinised because of the abortive mission to the ISS on October 11, which ended two minutes after take-off when a rocket failure forced its two-man crew to perform an emergency landing.
American Anne McClain, Canadian David Saint-Jacques and Russian Oleg Kononenko successfully took off from the Baikonur Cosmodrome in Kazakhstan on Monday on their way to the International Space Station.
The Soyuz is the only means of reaching the ISS since the United States retired the space shuttle in 2011.
Kononenko, McClain and Saint-Jacques were all smiles as footage broadcast by NASA TV showed them preparing to enter the Soyuz capsule before launch.
Soyuz heads to ISS on first manned mission since October failure
Speaking before the trip on Sunday, crew commander Oleg Kononenko affirmed his crew "absolutely" trusted the flight's preparation. The Russian rocket carries USA astronaut Anne McClain, Russian cosmonaut Oleg Kononenko? and CSA astronaut David Saint Jacques .
"We are psychologically and technically prepared for blastoff and any situation which, God forbid, may occur on board", said Kononenko, the 54-year-old crew commander, according to Radio Free Europe.
"Looking forward to having a full crew of six up here again, at least for a few weeks". It is the first mission since an aborted launch in October. "We feel very ready for it", she said.
A rehearsal unmanned flight, which delivered cargo including food and fuel supplies, was successfully carried out in mid-November.
If for some reason Russian Federation couldn't have resumed crewed flights on a timely basis, the space station's managers would have faced a hard choice over whether to leave the space station unoccupied for a time.
There, they'll meet the European Space Agency's Alexander Gerst, NASA's Serena Auñón-Chancellor and Roscosmos' Sergey Prokopyev, the current crew of the ISS who'll use the Soyuz to return to Earth on December 20.
Russian Federation said last month the October launch had failed because of a sensor damaged during assembly at the Baikonur cosmodrome, but insisted the spacecraft remained reliable.