This is the first time a private company has attempted to send a vessel to the space station, an act previously reserved for a small, elite group of government agencies.
Hawthorne-based SpaceX is run by PayPal's billionaire creator, Elon Musk.
Astronauts Donald Pettit and Andre Kuipers used the space station's robot arm to snare the Dragon after a few hours of extra maneuvering. The two vessels came together while sailing above Australia.
NASA is handing over routine orbital flights to private business so it can concentrate on grander destinations like asteroids and Mars.
Dragon took off from Cape Canaveral, Fla., on Tuesday and will remain at the space station for nearly a week. It will be freed next Thursday to return to Earth with a load of experiments and equipment.
Since the Dragon is a brand new type of vehicle and this is a test flight, NASA insisted on proceeding cautiously. A collision at orbital speed of 17,500 miles per hour could prove disastrous for the space station. Everything went perfectly, and two students in Southern California were watching very closely.
"It's really cool because not many high school students get to say that they have a project that is actually in space right now," said Paige D'Andrea.
D'Andrea and fellow student Max Holden attend Chaminade College Preparatory in West Hills. They came up with a science experiment that was selected to go up to the space station on the Dragon.
We all know that fermentation results in alcohol, but what happens if you do it in space without gravity?
"In space there is microgravity which puts it in a constant free fall and the constant free fall we believe will speed up the fermentation process," said Holden.
The experiment will be back on earth in about four weeks and the students will present their findings in Washington, D.C. at the Smithsonian's Air and Space Museum.
"I'm pretty sure it will work, I really hope it does work, that will be pretty cool," said Holden.
NASA officials say if all goes well, the space station crew plans to open Dragon's hatch Saturday. Then they will move that experiment along with others into the space station.
The Associated Press contributed to this report.