Using the station's 58-foot long (17.7-meter) robotic crane, NASA astronaut Don Pettit snared Dragon at 9:56 a.m. EDT (1356 GMT) as the two spacecraft soared 250 miles (400 km) over northwest Australia at 17,500 mph.
"It looks like we've got us a dragon by the tail," Pettit radioed to NASA Mission Control in Houston.
The capsule, built and operated by Space Exploration Technologies, or SpaceX, is the first of two new commercial freighters NASA will use to fly cargo to the $100 billion outpost following the retirement of the space shuttles last year.
The United States plans to buy commercial flight services for its astronauts as well, breaking Russia's monopoly on flying crews to the station.
Dragon blasted off aboard a SpaceX Falcon 9 rocket from Cape Canaveral Air Force Station on Tuesday. It is expected to be attached to a docking port on the station later on Friday.
The capsule is carrying about 1,200 pounds (544 kilograms) of food, water, clothing and supplies for the station crew. It will be repacked with equipment to come back to Earth and depart the station on May 31.
Splashdown in the Pacific Ocean off the coast of southern California would occur later that day.
(Reporting by Irene Klotz; Editing by Doina Chiacu)
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