The astronauts were the first sent to be sent to the space station since a crewed Soyuz launch was aborted in October after a booster rocket failed to separate properly, crippling the rocket.
The spacecraft has now docked at the space station following four orbits around the earth, NASA says.
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.
Plus, it's the first time a Canadian astronaut (Saint-Jacques) is headed to space since Chris Hadfield, who lead the International Space Station five years ago and was known for his publicity success.
The Soyuz MS-11 spacecraft docked with the ISS at 12:33 p.m. ET, following a six-hour journey from Baikonur Cosmodrome in Kazakhstan.
It was the first manned voyage 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 a harrowing emergency landing. Cosmonaut Kononenko said on Sunday, Dec. 2, during a press conference, that he "absolutely" trusts the flight plan.
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NASA spokesperson Gary Johnson described the mission as "textbook launch and insertion into orbit" during the liftoff commentary.
October's aborted trip saw two astronauts forced to make an emergency landing just minutes after take off. "We are psychologically and technically prepared for blast-off and any situation which, may occur on board".
As NPR's Bill Chappell reported in October, "The agency does have contracts with commercial companies like Boeing and SpaceX that are developing new vehicles to take astronauts up, but the first flights of those aren't scheduled until next year".
The Soyuz is the only spacecraft shuttling astronauts between Earth and the International Space Station since the US Space Shuttle was retired in 2011.
The crew will join American Serena Auñón-Chancellor, Germany's Alexander Gerst and Russia's Sergey Prokopyev, all of whom are already living on the orbital station.
Three astronauts have successfully blasted off to the International Space Station from Kazakhstan, a ideal launch that follows October's aborted mission.
Former astronaut Robert Thirsk said the schedule will be especially busy for the trio.