Mission official Enrico Palermo says it reached an altitude of 51 miles (82 kilometers) before beginning its gliding descent. "The spaceship was tested to its limits today and she performed just as we wished and we just couldn't be happier".
One of the two pilots handed Mr Branson a small Earth stress ball when the pair hugged after the spaceship landed safely after around an hour's journey.
Virgin Galactic considers 80km the boundary of space because it is used by the United States airforce and other USA agencies.
That differs from a long-held view that places the boundary at 62 miles.
But last month, the Fédération Aéronautique Internationale, which maintains world records for spaceflight, said it was considering adopting a 50-mile definition based on "compelling" scientific research that had recently been published.
Virgin's first experimental spacecraft failed during a 2014 test flight, with one of the pilots losing his life. He wouldn't estimate when commercial passenger trips might begin. "There is no guarantee that everything will work perfectly first time and, like all programs seeking to take bold steps, we will inevitably have times when things don't go as planned".
Two test pilots Mark "Forger" Stucky and former NASA astronaut Rick "CJ" Sturckow then hurtled the craft upward and out of sight. The space plane had a top speed of nearly three times the speed of sound and had a Mach 2.5 supersonic re-entry into the planet's atmosphere.
Mika Brzezinski Sorry for Pompeo 'Butt Boy' Comment
Anderson provided a list of alternative words Brzezinski might have used to describe Pompeo's conduct towards Saudi Arabia. Anderson suggested other phrasing: "I was with you, @morningmika , right up to the "butt boy" comment".
The FAA plans to formally honor the pilots of Thursday's flight by awarding them astronaut wings at a ceremony in Washington next year.
"Commercial space has great potential for American economic and innovative leadership", said FAA acting administrator Dan Elwell after the flight.
Richard Branson told reporters after the SpaceShipTwo test that commercial flights from Spaceport America could start in 2019 after as few as three more test flights. Also onboard the vehicle were four NASA-funded technology experiments, making this the first Virgin Galactic flight to generate revenue. I'm really looking forward to going up myself next year.' He said the ship was 'magnificent", declaring: "'Space is Virgin territory!' After that, it appears that the experience will be available to the public - for a hefty price of course.
But there were significant setbacks.
Virgin Galactic's VSS Unity supersonic plane successfully breached the edge of space during a flight today, the company has announced.
Virgin Space Ship Unity was released from a carrier aircraft and ignited its rocket engine.
SpaceX, the company owned by Elon Musk, is focused on carrying equipment for Nasa's programmes - although they do hope to take a Japanese billionaire around the moon by 2023.