The rocket ship hit an altitude of 82km before beginning its gliding descent, said mission official Enrico Palermo. It landed on a runway minutes later.
"But over the years, the price of crossing the Atlantic came down and down and down, and if we can get enough spaceships built and flying, I'm really hopeful that a lot of people watching your program one day will be able to go to space", he said.
While critics point to Branson's unfulfilled space promises over the past decade, the maverick businessman told a TV interviewer in October that Virgin's first commercial space trip with him onboard would happen "in months and not years".
Virgin Galactic, which is focused on space tourism, aims to use SpaceShipTwo to take paying customers for a short journey to and from space.
Virgin Galactic's chief, British billionaire Richard Branson, watched the flight from the ground. The flight was the first by the vehicle to cross the boundary of 50 miles, or approximately 80 kilometers, that USA government agencies use to award astronaut wings. But the long-held view is the boundary is 62 miles.
It had reached space altitudes around 50 minutes after take-off, which the company's Twitter account acknowledged with a tweet which read: "SpaceShipTwo, welcome to space". "Once we've gotten through that, we could start thinking about doing commercial flights", he said, not giving a specific number of test flights planned beyond "not a huge number".
The two pilots on board Virgin Galactic's spacecraft Unity became the company's first astronauts.
The aircraft reached an altitude of 271,268ft as it made its rapid ascent into space and clocked up a velocity equivalent to 2.9 times the speed of sound.
Virgin Galactic First Flight to Space Imminent
After the flight, the Federal Aviation Administration said it would award Unity's test pilots, Mark "Forger" Stucky and Frederick "CJ" Sturckow, with commercial astronaut wings.
In addition to the test pilots, a flight test dummy and four research payloads from NASA's Flight Opportunities Program were on board to help simulate the weight distribution of having passengers on board.
The high-altitude launch is the first commercial USA flight beyond the atmosphere since 2011 - and a major advance for civilian space travel.
Virgin Galactic has successfully sent a spacecraft to the edge of space.
VSS Unity's feat represents a major step forward for Virgin Galactic's ambition - in tandem with The Spaceship Company, which built it - to take passengers into space on $250,000 sub-orbital joyrides, during which they will...
But delays and a fatal crash in 2014 prevented Sir Richard's original ambitions. SpaceX's Elon Musk recently announced plans to take a wealthy Japanese entrepreneur and his friends on a trip around the moon.More news: Nasa's Voyager 2 probe reaches interstellar space