SpaceX Dragon spacecraft flying formation with International Space Station. Image: NASA

"Looks like we've got a Dragon by the tail," said NASA astronaut Don Pettit.

The SpaceX Dragon capsule safely berthed to the International Space Station today, greeted by cheers in mission control and pronouncements about how a new era is beginning in orbit.

The Dragon did something that has happened dozens of times before - made a successful rendezvous with the space station to deliver supplies. But it's the first privately-owned spacecraft to make the trip.

"It's been a long time coming," said Mike Suffredini, NASA's space station program manager, this afternoon. "I can't tell you how proud we are to have been a part of this historic moment."

"We're incredibly excited," said Elon Musk, the founder and head of SpaceX. "There's so much that could have gone wrong and didn't."

NASA hopes private American companies will inexpensively deliver supplies, and eventually astronauts, to the station, something the U.S. has been unable to do without foreign help since the space shuttles were retired last year.

NASA TV

The berthing was done achingly slowly - standard procedure when two ships fly together in orbit at more than 17,000 miles per hour.  Rather than let the Dragon maneuver itself for a docking, astronaut Pettit reached out with the station's robot arm to grab the approaching ship.

NASA TV

NASA said under current plans, Dragon will remain docked to the space station for unloading until May 31.  After undocking, SpaceX will order the ship to re-enter the atmosphere and splash down in the Pacific off the Southern California Coast.

NASA TV

"This is a fantastic thing," said Musk, surrounded by cheering SpaceX employees in California, "but there are better things to come in the future."