Astronauts Doug Hurley and Bob Behnken arrived after a 19-hour journey that began from Kennedy Space Center with a liftoff that represented a number of firsts.
It was the first time Elon Musk's space company – or any private firm – had put humans into space, as well as the first time astronauts have left from US soil since the end of the Space Shuttle programme in 2011.
The space station orbits at around 220 miles above the planet, and the floating laboratory will serve as a home for the two astronauts over the coming months, during which further tests will be conducted on the Crew Dragon capsule that carried them there.
Nasa administrator Jim Bridenstine tweeted "welcome home" the pair. "America's two favorite dads in space have docked to the Space Station," he wrote.
The spacecraft had to perform a series of manoeuvres to raise its obit to come close enough to dock at the space station.
The Dragon docked autonomously to a port on the bow section of the of the station's Harmony module.
Once the Dragon is sealed in place and pressure checks are completed, the hatch door will open and Mr Hurley and Mr Behnken will join the three other space station residents, Nasa's Chris Cassidy and Russia's Anatoli Ivanishin and Ivan Vagner, to become members of the Expedition 63 crew.
The aim of the mission is to demonstrate SpaceX's ability to ferry astronauts to the space station and back safely.
It is the final major step required by SpaceX's astronaut carrier, the Crew Dragon, to get certified by Nasa's Commercial Crew Programme for long-term manned missions to space.
The mission is expected to last anything between one and four months.