Astronauts at the ISS have now boarded the capsule of the Dragon, which carried a dummy pilot and 90kg (200lbs) of supplies on its test flight.
On Saturday, President Donald Trump praised the historic launch of Demo-1, a critical step for NASA and SpaceX to demonstrate the ability to safely fly missions with NASA astronauts to the orbital laboratory.
Applause and cheers broke out at SpaceX's control center in Hawthorne, California as Crew Dragon attached itself to the ISS, Space.com reported.
"Congratulations to all nations, private space firms and individuals who wake up every day driven by the magic of exploration", American astronaut Anne McClain, the third crew member on the station, said at a welcoming ceremony broadcast over NASA TV.
SpaceX celebrated the successful launch of its Crew Dragon capsule followed by the successful autonomous docking of the spacecraft at the International Space Station on the weekend as aprelude to the resumption of manned USA space flights, possibly in the next year.
The entire procedure was light on showmanship compared to SpaceX's last major flight test, when the company launched a red Tesla into space on its Falcon Heavy rocket.
Dragon will remain at the space station until Friday, when it undocks and aims to splashdown in the Atlantic ocean, a few hundred miles off the Florida coast. SpaceX's new crew capsule arrived at the International Space Station on Sunday, acing its second milestone in just over a day.
"Today's successful launch marks a new chapter in American excellence, getting us closer to once again flying American astronauts on American rockets from American soil", NASA administrator Jim Bridenstine wrote in a statement.
SpaceX successfully launches Crew Dragon
"We are not in a space race", he said.
"The Crew Dragon is a fundamental redesign, with hardly a part in common with Dragon", SpaceX founder Elon Musk said early Saturday morning, after the launch, during a news briefing. Russian Soyuz seats go for up to $82 million apiece.
The only way astronauts can get to space are via Russian rockets, yet the cost of using them has steeply risen over the years.
That said, the Crew Dragon is also created to be an enjoyable ride. "We've got to dock to the space station and come back".
There was, however, no crew aboard the spacecraft, just a test dummy named Ripley, in a nod to the lead character in the Alien movies.
Ripley was joined in the ship's maiden flight by Little Earth - a plush toy which looks like the Earth with arms and legs.
Next up, though, should be Boeing, NASA's other commercial crew provider.More news: Women's race delayed after rider catches up to men
More news: Samsung Galaxy S10+, S10, S10e to Be Launched in India Today
More news: Michael Jackson documentary fallout prompting music ban from radio stations