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. Monday while flying over 250 miles above Ecuador.
On Oct. 11, a rocket failure forced a Soyuz capsule carrying two astronauts to abort and make an emergency landing.
NASA and Roscosmos said that all onboard systems were operating normally and the crew was feeling fine.
Expedition 58 Flight Engineer David Saint-Jacques of the Canadian Space Agency (CSA), top, Flight Engineer Anne McClain of NASA, center, and Soyuz Commander Oleg Kononenko of Roscosmos, bottom, wave farewell prior to boarding the Soyuz MS-11 spacecraft for launch in Baikonur, Kazakhstan, on December 3, 2018.
Astronauts of the first manned space mission since an unprecedented accident in October on Sunday brushed aside concerns about Russia's Soyuz rocket, saying risks were part of the job.
European Space Agency astronaut Alexander Gerst, NASA's Serena Aunon-Chancellor and Sergei Prokopyev of Roscosmos will greet the trio when they arrive at the ISS.
If all goes to plan, the spacecraft is due to dock at the ISS at just after 5.30pm tonight - six hours after lift-off.
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Kononenko, McClain and Saint-Jacques smiled and gave thumbs up to the cheering crowd including relatives as they ascended into the Soyuz capsule on Monday morning. They managed to emerge safely despite the harrowing ordeal. Russian investigators blamed the malfunction on a damaged sensor.
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.
Russian space officials took measures to prevent the repeat of such a rocket failure.
NASA announced Monday that Hague and Ovchinin will now launch to the space station on February 28, along with NASA astronaut Christina Hammock Koch.
Monday marks two important milestones for the Soyuz rocket.
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.
The launch of the rocket will be observed by the head of Roscosmos, Dmitry Rogozin, the head of NASA's manned flights department, William Gerstenmayer, and the governor-general of Canada, Julie Peyette (former astronaut of the Canadian Space Agency).