Elon Musk’s SpaceX is a giant step closer to launching astronauts into space after the world’s first private, unmanned, passenger rocket docked at the International Space Station on Sunday.

SpaceX’s Dragon capsule, America’s newest capsule for astronauts, launched Saturday on its first test flight, with only an instrumented dummy.

But the three station astronauts had front-row seats as the sleek, white vessel neatly docked at 10.51pm (Australian time) more than 400 kilometres above the earth’s surface, north of New Zealand.

“We can confirm hard capture is complete,” NASA announced.

The Dragon capsule became the first American-made, designed-for-crew spacecraft to pull up in eight years.

SpaceX has been developing Crew Dragon since 2014 under a $2.6 billion contract with NASA.

After a successful landing, retired astronaut Scott Kelly, NASA’s former one-year space station resident, tweeted “Giant leaps are made by a series of consistent smaller steps. This one will be a big step!”

The first @Commercial_Crew mission arrived at the space station today when the @SpaceX #CrewDragon completed soft capture on the Harmony module at 5:51am ET. #LaunchAmerica https://t.co/Bgcgac0O50 pic.twitter.com/KfNFpHxpGx

— International Space Station (@Space_Station) March 3, 2019

NASA Administrator Jim Bridenstine called Dragon “a new generation of space flight”.

“Congratulations to all for this historic achievement getting us closer to flying American Astronauts on American rockets,” he tweeted.

Dragon will spend five days docked to the orbiting outpost, before splashing down in the Atlantic Ocean, off the coast of Florida, next Friday.

If the six-day demo goes well, SpaceX could launch two astronauts this summer under NASA’s commercial crew program.

Astronauts – Doug Hurley and Bob Behnken – were at SpaceX Mission Control in Southern California, observing all the action.

They rushed there from Florida after watching the Dragon rocket into orbit early Saturday from NASA’s Kennedy Space Center.

“Just super excited to see it,” Mr Behnken said minutes after the link-up.

“Just one more milestone that gets us ready for our flight coming up here.”

While SpaceX has sent plenty of cargo Dragons to the space station, crew Dragon is a different beast. It docked autonomously under the station astronauts’ watchful eyes, instead of relying on the station’s robot arm for berthing.

Mr Behnken said that’s the way it should work when he and Mr Hurley are on board; they may push a button or two and will have the ability to intervene, if necessary.

As part of Sunday’s shakedown, the station astronauts sent commands for the Dragon to retreat and then move forward again, before the capsule closed in for good.

SpaceX employees at company headquarters in Hawthorne, California, cheered and applauded as crew Dragon pulled up and docked at the orbiting lab.

They burst into applause again, several minutes later, when the Dragon’s latches were tightly secured.

The station astronauts offered congratulations to SpaceX, as they got ready to open the hatches and collect the supplies stashed aboard Dragon.

The capsule’s lone passenger – a mannequin wearing a white SpaceX spacesuit – also was going to be welcomed aboard.

The test dummy – or Smarty as SpaceX likes to call it, given all the instrumentation – is named Ripley after the lead character in the science-fiction “Alien” films.

-With AAP