The berthing marked the climax of the California-based company's demonstration mission
SpaceX became the first commercial outfit to send its own cargo capsule to the International Space Station, heralding the start of a new era for private spaceflight.
The berthing marked the climax of the California-based company's demonstration mission to become the first to restore US access to the space outpost after NASA retired the three-decade shuttle program last year.
With no humans on board, the Dragon capsule is delivering about a half ton of supplies and science experiments for the ISS, and aims to return a slightly larger load of gear to Earth on May 31.
"There was so much that could have gone wrong, and it went right," SpaceX chief executive Elon Musk, a billionaire Internet entrepreneur, told reporters after the berthing was complete.
"This is really going to be recognized as a significantly historical step forward in space travel, and hopefully the first of many to come."
The Dragon is toting 521 kilograms (1,148 pounds) of goodies for the space lab, including food, supplies, computers, utilities and science experiments. It plans to return a 660-kilogram load to Earth.
The hatches are set to open at 7:40 am (1140 GMT) on Saturday so that the unloading can begin, NASA said.
"It looks like we got us a Dragon by the tail," said US astronaut Don Pettit, who was operating the Canadian-built robotic arm from the space station as it reached out and captured the unmanned SpaceX capsule at 9:56 am (1356 GMT).
The capsule was installed on the station's Harmony module by European Space Agency astronaut Andre Kuipers at 11:52 am (1552 GMT), and the berthing was complete when NASA astronaut Joe Acaba bolted the Dragon on at 12:02 pm (1602 GMT), NASA said.
"I can't tell you how proud we are to have been a part of this historic moment," said ISS program manager Mike Suffredini, adding that the spacecraft had "performed nearly flawlessly" since its launch on Tuesday from Cape Canaveral, Florida.
John Holdren, assistant to President Barack Obama for science and technology policy, hailed the mission as "an achievement of historic scientific and technological significance and a key milestone in President Obama's vision for America's continued leadership in space."
The US space shuttle program ended in 2011, leaving only Russia capable of carrying astronauts and cargo to the ISS and back to Earth.
The space agencies of Japan and Europe have supply ships that can ferry cargo to the ISS but cannot return to Earth intact, and those missions are set to end in the coming years, Suffredini said.
That means SpaceX and its competitor Orbital Sciences Corporation would become the chief cargo servicers of the $100 billion space station, which is set to remain operational until 2020.
"Between those two spacecraft, they will supply the lion's share of the cargo to the International Space Station for the life of the station," Suffredini said.
The berthing mission opens the way for SpaceX's $1.6 billion contract with NASA to supply the space station and return cargo to Earth in 12 missions over the coming years.
Suffredini said the next cargo supply mission by SpaceX is tentatively set for September.
Orbital Sciences also has a $1.9 billion contract with NASA to supply the space station and is scheduled for its first test flight in August, followed by a demonstration mission to the ISS in December, Suffredini said.
SpaceX hopes its gumdrop-shaped Dragon capsule will be able to carry astronauts to the ISS in about three years' time. Until then, US astronauts must pay Russia about $63 million per seat aboard the Soyuz.
SpaceX and a handful of other companies are using their own funds but are also being helped in their endeavors with seed money from NASA to build cargo and crew capability.
SpaceX is the brainchild of Musk, a 40-year-old billionaire who made his fortune founding a company that later merged with the PayPal online service, bought by Internet auction giant eBay for $1.5 billion in 2002.
Today he leads SpaceX, Tesla Motors -- a venture marketing electric cars -- and SolarCity, a company that makes solar panels for homes and businesses.
Musk said alcohol had been prohibited from the Hawthorne, California headquarters -- where the average age of SpaceX employees is 30 -- until the berthing mission was complete.
"But now that things are good I think we will probably have a bit of champagne and have some fun, yeah," he said to hoots and hollers from employees gathered around.
"It is best to be very sober in these circumstances until the deed is done."