The Crew Dragon launched on Saturday, May 30, from the Kennedy Space Center Launch Complex 39A in Florida, US.
NASA’s astronauts then coasted through space for about 19 hours before reaching the ISS some 262 miles above Earth.
Despite the thrill of the ride, Mr Hurley said the two astronauts still got about seven hours of sleep on the way up.
The astronauts will now get to work on the ISS, joining the ranks of ISS Expedition 63.
While in orbit, they will help their fellow astronauts in maintaining the station as well as carry out scientific experiments and tests.