The "Resilience" spacecraft docked autonomously with the space station some 400 kilometres above the Midwestern US state of OH at 11:01pm on Monday (04:01 GMT Tuesday), completing a 27.5-hour journey.
The US space agency hopes the launch will mark the beginning of many regular crew flights to the space station from the United States, according to Deutsche press agency (dpa). The rotation will continue until Boeing joins the programme with its own spacecraft late next year.
Most nations with advanced space capabilities are turning to rope in the private sector for more cost-efficient "functional" space operations-involving satellite launches to the low Earth orbit, unmanned and manned space missions to the ISS, etc-as they devote their public space brawn to space exploration.
As they prepared for the space station link-up, the Dragon crew beamed down live-window views of New Zealand and a brilliant blue, cloud-streaked Pacific 400km below.
Their Demo-2 mission represented the first manned launch from U.S. shores in almost a decade and the first time a private firm, rather than a government space agency, sent people into orbit.
At the end of its missions, the Crew Dragon deploys parachutes and then splashes down in water, just as in the Apollo era.
Besides ending reliance on Russia's Soyuz spacecraft for getting crews to and from the station, commercial crew vehicles like Crew Dragon will enable the station to support seven-person crews for long-duration missions.
Victor Glover, a 1999 general engineering graduate of Cal Poly, piloted SpaceX's Crew-1 Dragon capsule to the ISS alongside NASA astronauts Mike Hopkins and Shannon Walker, and Japanese astronaut Soichi Noguchi.
SpaceX founder and CEO Elon Musk did not attend Sunday's launch after announcing last week that he had received contradictory results on four separate coronavirus tests.
He said two tests came back positive but two other tests came back negative.
'Looks fantastic, ' Mission Control radioed from SpaceX headquarters in Hawthorne, California.
"It was a very nice night onboard Resilience", Hopkins replied from the capsule, traveling in orbit at roughly 17,500 miles (28,160 km) per hour.