The mission, codenamed Ax-1, was launched on SpaceX's Falcon 9 rocket from Kennedy Space Center of National Aeronautics and Space Administration (NASA) in Florida on Friday.
The four-person multinational crew is composed of Commander Michael Lopez-Alegria and Pilot Larry Connor of the United States, Mission Specialist Eytan Stibbe of Israel, and Mission Specialist Mark Pathy of Canada.
It is the first mission with an entirely private crew to arrive at the ISS, said NASA.
Ax-1 docked to the orbital complex at 8:29 a.m. Eastern Time on Saturday (0029 GMT on Sunday) while the spacecraft was flying 260 miles (about 418 km) above the central Atlantic Ocean, according to NASA.
During the 10-day mission, the crew will conduct scientific research, outreach and other activities, according to NASA.