Canadian Space Agency president Sylvain Laporte told the crew members there was "a lot of relief" when the astronauts entered the space station about two hours after docking.
Monday's launch was needed to guarantee that the ISS was not left unmanned after the station's current crew returns to earth later this month.
Canadian astronauts Bob Thirsk and Jenni Sidey-Gibbons watched the launch of astronaut David Saint-Jacques for the global space station from Kazakhstan at the Canadian Space Agency headquarters Monday, December 3, 2018 in St. Hubert, Que.
A Russian Soyuz spacecraft carrying three astronauts successfully docked with the International Space Station on Monday following a clean launch from the Baikonur Cosmodrome in Kazakhstan six hours earlier.
They will head to the ISS after a Soyuz rocket carrying Russia's Aleksey Ovchinin and USA astronaut Nick Hague failed on Oct 11 just minutes after blast-off.
Last month, Roscosmos tweeted a video of the October 11 failed Soyuz rocket launch that forced NASA astronaut Nick Hague and Russian cosmonaut Alexey Ovchinin into making a harrowing emergency landing. They'll be greeted by current occupants Alexander Gerst of the European Space Agency, NASA's Serena Auñón-Chancellor and Roscosmos' Sergey Prokopyev, who are scheduled to then ride the Soyuz back to Earth on December 20.
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McClain, Saint-Jacques and Kononenko will spend more than six months at the space station doing research and experiments in biology, Earth science, physical sciences and technology. They managed to emerge safely despite the harrowing ordeal.
Russian investigators blamed that malfunction, which occurred as the first and second stages of a booster rocket separated, on a damaged sensor.
NASA astronaut Nick Hague and Russian cosmonaut Alexey Ovchinin ejected the capsule from the rocket when the spacecraft was about 50 kilometers - 31 miles - above Earth.
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.
They escaped unharmed but the failed launch - the first such incident in Russia's post-Soviet history - raised concerns about the state of the Soyuz programme.
After Monday's successful launch, NASA Administrator Jim Bridenstine tweeted his thanks to his Russian counterpart Dmitry Rogozin and to NASA and Roscosmos space teams "for their dedication to making this launch a success".