Of the trio set to reach the ISS six hours after blastoff, both Saint-Jacques and McClain will fly for the first time.
NASA astronaut Anne McClain, David Saint-Jacques of the Canadian Space Agency and Oleg Kononenko of Russian space agency Roscosmos docked with the station at 11:33 p.m. (1723 GMT; 12:33 p.m. EST) Monday.
Speaking in French, he described his first sunrise seen from space as "breathtaking".
The first manned space mission to the International Space Station since an unprecedented accident in October, which raised concerns about Moscow's Soviet-designed spacecraft, will launch on Monday.
Canada's governor general and former astronaut Julie Payette is expected to be among dignitaries to watch Monday's launch.
He said Ovchinin and Hague would be on board, along with NASA's Christina Koch.
The crew reported that all went well in the critical initial minutes after liftoff.
The Soyuz accident in October was the first aborted crew launch for the Russian space program since 1983, when two Soviet cosmonauts safely jettisoned after a launch pad explosion.More news: Trump Says China Has Agreed to Reduce, Remove Tariffs on Cars
Innovation Minister Navdeep Bains praised the successful takeoff and said the mission offers an exciting opportunity for scientific research and developments that could have broad applications, in such things as robotics and aging.
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. They will spend in space for 194 days.
Astronaut Jenni Sidey-Gibbons echoed the message, saying Saint-Jacques was a special role model for her and other young people who may be considering a future in space.
It was the first manned launch for the Soviet-era Soyuz since October 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. They managed to emerge safely despite a harrowing descent back to Earth.
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.
NASA astronaut Anne McClain, David Saint-Jacques of the Canadian Space Agency and Oleg Kononenko of Russian space agency Roscosmos were greeted upon arrival Monday by the station's current crew members, who had waited outside the capsule's hatch.
NASA also repeatedly dispelled drama between the two space agencies in the past, promising continued cooperation.
Kononenko, McClain, and Saint-Jacques will officially become the Expedition 58 crew when Gerst, Aunon-Chancellor and Prokopyev depart the station for home on December 20.