After taking off around 2:50 a.m. EST on Saturday, the capsule docked just before 6 a.m. Sunday, about 27 hours after liftoff. It will be docked there for five days.
It is the first time a commercially built spacecraft has docked with the International Space Station.
The unmanned Dragon spacecraft, blasted from the Kennedy Space Center in Cape Canaveral, Florida, is scheduled to plop down in the Atlantic Ocean on March 8.
A life-sized dummy named Ripley, after the lead character in the "Alien" movies, was the capsule's only passenger.
The launch and docking were broadcast live on NASA TV.
NASA has since turned to SpaceX and Boeing, providing them with $8 billion, to help get astronauts to the ISS, which is about 250 miles about Earth. Currently, Russian Soyuz rockets are the only means by which to reach the space station, and NASA, according to the AP, pays $82 million per seat.
Boeing is planning to test its Starliner capsule in April, potentially with people aboard as early as August.
Bridenstine said it's only a matter of time before astronauts are being carried into space aboard Dragons or Starliners.
"We are not in a space race," he told the AP. "That race is over. We went to the moon and we won. It's done. Now we're in a position where we can take our time and make sure we get it right."