Running ahead of schedule, station commander Oleg Kononenko and flight engineer Don Pettit opened the hatch to Dragon just before 6 a.m. EDT (1000 GMT), NASA mission commentator Josh Byerly reported from Mission Control in Houston.
The bell-shaped capsule, which was making its second test flight, arrived at the space station on Friday.
The crew wore protective masks and goggles, but the interior of Dragon, which is 350 cubic feet (10 cubic meters), about the size of a large walk-in closet, proved clean.
"There was no sign of any kind of (debris) floating around," Pettit radioed to Mission Control, adding that Dragon "smells like a brand new car."
"It looks like it carries about as much cargo as I could put in my pickup truck," Pettit later told reporters during an in-flight press conference.
"There's not enough room in here to hold a barn dance, but for transportation of crew up and down through Earth's atmosphere and into space, which is a rather short period of time, there's plenty of room in here for the envisioned crew," Pettit said.
Space Exploration Technologies, or SpaceX, is working on a seven-passenger version of Dragon, which could be ready for test flights in 2015.
The capsule at the space station carries about 1,200 pounds (544 kg) of food and other supplies for the station, all non-essential items because NASA and SpaceX did not know beforehand if it would actually make it to the station.
Following Tuesday's launch aboard a SpaceX Falcon 9 rocket from Cape Canaveral Air Force Station in Florida, Dragon had to demonstrate that it could be commanded and controlled by operators on the ground as well as by the orbiting space station crew.
Dragon and SpaceX mission control in Hawthorne, California, aced two days of precision flying and systems tests, clearing the way for Dragon to fly within reach of the station's 58-foot (17.7 meter) robot arm on Friday.
Astronauts snared the capsule at 9:56 a.m. EDT (1356 GMT) Friday as the two spacecraft zoomed around the planet at 17,500 mph (28,164 kilometers per hour). It was anchored into a berthing port on the station's Harmony connecting node a few hours later.
"You made history today and it firmly locked us into place and locked the future direction of the American space program in place," NASA administrator Charlie Bolden radioed to the crew later on Friday.
NASA's use of commercial spaceships to fly cargo - and eventually astronauts - to and from the station will ""revolutionize the way we carry out space exploration," Bolden added.
SpaceX and a second company, Orbital Sciences Corp, hold NASA contracts worth a combined $3.5 billion to fly cargo to the station.
Orbital plans to debut its Antares rocket and Cygnus capsule later this year.
NASA is reviewing proposals from at least four firms, including SpaceX, seeking funding under a related program to develop spaceships for flying astronauts as well. Awards are expected in August.
Since the retirement of the space shuttles last year, the United States is dependent on Russia to fly crews to the station, a $100 billion project of 15 nations. It hopes to break the Russian monopoly, which costs NASA about $400 million a year, in 2017.
Once unloaded, Dragon will be filled with about 1,300 pounds (590 kg) of equipment and science gear that need a ride back to Earth - the first big return load since the final shuttle flight last July.
Dragon is due to depart the station on Thursday and splash down in the Pacific Ocean about 250 miles off the coast of southern California later that day.