The craft launched on Tuesday from the Baikonur Cosmodrome in Kazakhstan at 9.30pm BST and arrived at its destination a mere five hours and 38 minutes later at 2.57am BST.
A Russian Soyuz rocket gave a flawless launch sequence and the crew made their journey in a Soyuz MS-06 space capsule.
As the rocket launched a translator for Russia’s Mission Control Centre in Moscow announced during the live broadcast: “Everything is nominal on board [and] the crew is doing fine.”
The craft arrived at the International Space Station a couple of minutes early.
NASA TV commentator Rob Navias said during the launch: “A series of burns over the next several hours will gradually raise their orbit as they chase down the space station.”
The crew consisted of two NASA astronauts, Mark Vande Hei and Joe Acaba and one Russian cosmonaut, Alex Misurkin.
They are meeting up with the other half of Expedition 53 at who arrived at the station in July.
They include NASA astronaut Randy Bresnik, Russian cosmonaut Sergey Ryazanskiy and European Space Agency astronaut Paolo Nespoli.
Mr Vande Hei, Mr Acaba and Mr Misurkin will spend five months aboard the station.
NASA officials said in a statement that they are going to: “Perform hundreds of experiments in biology, biotechnology, physical science and Earth science.”
They will serve as members of Expeditions 53 and 54 during their stay.
This is Mr Vande Hei’s first time in space, whereas Mr Acaba and Mr Misurkin have flown to the space station before.
Mr Misurkin served as a flight engineer during Expedition 35/36 in 2013, and Mr Acaba was a flight engineer for Expedition 31/32 in 2012.