The billionaire businessman smiled as he headed back to the planet surface after feeling the thrill of weightlessness for several minutes on Sunday afternoon.
The launch was hailed a “landmark moment” for the billionaire businessman, as well as the whole commercial space industry.
Take-off had been delayed by about 90 minutes on Sunday due to the weather overnight at Spaceport America in New Mexico, in the US.
But video streamed live online showed the Virgin Galactic in the air at about 3.45pm UK time, and the aircraft had reached 40,000 feet by 4pm.
The spacecraft was carried up into the atmosphere by its mothership before being released so it could power up to highs of 250,000 feet.
Sir Richard and his crew reached speeds of Mach 3 on their way to the edge of space.
After a short spell during which they experienced weightlessness, the craft then pointed downwards and made its way back to the ground, touching down around 4.40pm.
On the return flight, Sir Richard hailed the “experience of a lifetime” and the “hard, hard work” that went into the flight.
Sir Richard is the first owner-astronaut to take part in a mission, beating Amazon founder Jeff Bezos, who plans to reach space in his own rocket through his Blue Origin company.
On the ground, Michael Colglazier, chief executive of Virgin Galactic, said: “This is a landmark moment for Virgin Galactic.
“It’s a landmark moment for the new commercial space industry and it certainly is a landmark moment for our founder Richard Branson.”
He said the company’s work on Sunday was dedicated to “opening up space to all”.
Tourists are expected to pay 250,000 US dollars (£180,000) for a spaceflight on Virgin Galactic, which includes four minutes of zero gravity.