The firm’s Falcon rocket, topped by an unmanned Dragon freight capsule, lifted clear of its Florida pad at 03:44 EDT.
The initial climb to an altitude some 340 km above the Earth lasted a little under 10 minutes.
Within moments of being ejected, Dragon opened its solar panels.
It will take a couple of days to reach the station. The plan currently is for the vessel to demonstrate its guidance, control and communications systems on Thursday, at a distance of 2.5 km from the International Space Station (ISS).
If those practice proximity manoeuvres go well, Dragon will be allowed to drive to within 10 m of the station on Friday. Astronauts inside the platform will then grab the ship with a robotic arm and berth it to the 400 km-high structure.
They will empty Dragon of its 500 kg of food, water and equipment, before releasing it for a return to Earth at the end of the month.
The mission has major significance because it marks a big change in the way the US wants to conduct its space operations.
NASA is attempting to offload routine human spaceflight operations in low-Earth orbit to commercial industry in a way similar to how some large organizations contract out their IT or payroll.
The carriage of freight will be the first service to be bought in from external suppliers; the transport of astronauts to and from the station will be the second, later this decade.
The US agency hopes these changes will save it money that can then be invested in exploration missions far beyond Earth, at destinations such as asteroids and Mars.
SpaceX has many new systems it has to demonstrate in the coming days, and has tried to lower expectations ahead of the mission.
NASA has set the California company a series of development milestones. Only when those have been met fully will a $1.6 billion ISS re-supply contract kick in.
The agency is also looking to engage a second cargo partner. Orbital Sciences Corporation of Virginia is slightly behind SpaceX in its development schedule, although it started work on its Antares rocket and Cygnus capsule system later. Orbital expects to fly a first mission to the vicinity of the ISS later this year or early in 2013.
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