The UK entrepreneur flew high above New Mexico in the US in the vehicle that his company has been developing for 17 years.
The trip was the "experience of a lifetime", he said. He returned safely to Earth just over an hour after leaving the ground.
"I have dreamt of this moment since I was a kid, but honestly nothing can prepare you for the view of Earth from space," he said in a press conference following the flight. "The whole thing was just magical."