The spacecraft attached to ISS via "soft capture" at 5:51 a.m.
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. Getting those spacecraft flying would mark the restoration of a USA crew-launching capability that was lost when the space shuttle fleet was retired in 2011. The former astronaut said he was heartened to see that the new propulsion, communication, and other systems on Crew Dragon all were performing as expected so far, with the biggest tests yet to come with docking to the station, and reentry through Earth's atmosphere. Dragon 1, which has been flying cargo resupply missions to the ISS since 2012, only maneuvered close enough to be grappled by the station's robotic arm, which then moved the spacecraft into position to be berthed.
The successful demonstration brings the USA one step closer to once again sending people into orbit without relying on Russian space vehicles, which have ferried American astronauts to the International Space Station since NASA retired its shuttles in 2011.
Jim Bridenstine, head of the USA space agency, has explained NASA wants to reduce costs in low orbit to devote resources to getting back to the Moon and constructing a small space station in lunar orbit in the 2020s.
Ever since NASA retired the space shuttle in 2011, the US has been hitching rides to and from the space station aboard Russian Soyuz spacecraft.More news: Former Voice contestant Janice Freeman dies aged 33 from a blood clot
The three U.S., Canadian and Russian crew members aboard the space station watched the rendezvous via TV cameras. The dates of the start of flights by both companies were repeatedly postponed.
This test flight didn't include crew - except for a high tech mannequin named "Ripley" - but it was meant to go through all the procedures of a crewed mission.
Looking on from Kennedy's Launch Control were the two NASA astronauts who will strap in as early as July for the second space demo, Doug Hurley and Bob Behnken.
NASA Administrator Jim Bridenstine said, "What today really represents is a new era in space flights".
"There is nothing more important for us than this endeavour, and we really appreciate the opportunity from Nasa to do this".
SpaceX's Crew Dragon can now check another milestone off its list. Musk is also the CEO of electric carmaker Tesla.
If the test goes to plan, it will be approved to carry people.