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.
A Soyuz MS-11, carrying one astronaut each from the USA and Canada and a cosmonaut from Russian Federation, has been successfully launched to the International Space Station (ISS) on Monday and has safely reached orbit, the United States space agency NASA said in a statement.
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.
Anne McClain, a 39-year-old former military pilot, struck a similar note.
NASA's Anne McClain, Russia's Oleg Kononenko, Canada's David Saint-Jacques were aboard the launch from the Baikonur Cosmodrome on Monday as part of Expedition 58. Eastern, Saint-Jacques and his two crewmates floated in from the docked Soyuz capsule, embracing the astronauts who have been at the space station since June.
The International Space Station is about to receive some company: a Russian Soyuz rocket and new crew successfully traveled to space on Monday.
The Soyuz is the only spacecraft shuttling astronauts between Earth and the International Space Station since the US Space Shuttle was retired in 2011.
She said the most unsafe moments will come in the moments following the launch, as the rocket passes through several "critical zones" on its way into space.
The crew repeatedly denied being nervous about flying and insisted the fact that the two-man crew had safely returned to Earth despite the dramatic mishap had demonstrated the reliability of the rocket's safety mechanisms.
It will be the first flight for both McClain and Saint-Jacques and the fourth for Kononenko.
The arrival of the three astronauts restores the space station's crew to six as they join Serena Aunon-Chancellor of NASA, Alexander Gerst of the European Space Agency and Sergey Prokopyev of Roscosmos, who are scheduled to remain aboard until December 20. They managed to emerge safely from a harrowing ordeal.
In October, a Soyuz launch failed, forcing the 2 crewmembers to make an emergency landing.
Investigators blamed a faulty sensor which they said had been damaged during assembly at the Kazakh site.
Russian space officials have taken measures to prevent the repeat of such incidents.
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".