"This is just the beginning of what we can do to support human space flight," Orbital executive vice president Frank Culbertson, a retired NASA astronaut, told reporters after Cygnus went into orbit around the Earth.
The Cygnus capsule, hitched to Orbital Science's Antares rocket, blasted off at 10:58 am (1458 GMT) from NASA's Wallops Flight Facility off Virginia's eastern coast, for a Sunday rendezvous with the ISS.
At the orbiting outpost, the Exhibition 37 crew watched live video of the blast-off.
"Congrats @OrbitalSciences -- great launch! Excited for Cygnus arrival on Sunday!" Nyberg tweeted using her handle @AstroKarenN.
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Cygnus separated from the rocket's second stage about 10 minutes after blast-off to reach Earth's orbit, marking the success of the launch. It later deployed both of its solar arrays, which will supply power to the spacecraft.
The payload separation was successful, a NASA commentator said on the US space agency's live television feed. Clapping could be heard at mission control.
"All going very smoothly with the continuing health of the spacecraft."
Cygnus will ferry about 1,300 pounds (590 kilograms) of food, clothing and other cargo for the crew aboard the space station, which it is scheduled to reach at 1130 GMT Sunday.
"Today marks a milestone in our new era of exploration as we expand the capability for making cargo launches to the International Space Station from American shores," NASA Administrator Charles Bolden said in a statement.
"Orbital's extraordinary efforts are helping us fulfill the promise of American innovation to maintain our nation's leadership in space."