The powered test flight over California's Mojave Desert lasted 16 seconds and broke the sound barrier.
"It was stunning," Branson told Reuters. "You could see it very, very clearly. Putting the rocket and the spaceship together and seeing it perform safely, it was a critical day."
The spaceship and its carrier aircraft, WhiteKnightTwo, took off from the Mojave Air and Space Port at 7 a.m. PDT (10.00 a.m. EDT), heading to an altitude of about 46,000 feet, where SpaceShipTwo was released.
Two pilots then ignited the ship's rocket engine and climbed another 10,000 feet, reaching Mach 1.2 in the process. Additional test flights are planned before the spaceship will fly even faster, eventually reaching altitudes that exceed 62 miles.
"Going from Mach 1 to Mach 4 is relatively easy, but obviously we've still got to do it. I think that the big, difficult milestones are all behind us," Branson said.
Virgin Galactic is selling rides aboard SpaceShipTwo for $200,000 per person. More than 500 people have put down deposits.
Branson and his grown children plan to be the first non-test pilots to ride in the spacecraft, about a year from now.