SpaceShipTwo took off at the Mojave test centre in California on Thursday. Around 50 minutes later, it reached space. The aircraft reached an altitude of 271,268ft before making its descent back to earth.
Sir Richard applauded and cheered as SpaceShip Two touched back down at the test centre.
The passenger rocket reached a height beyond the altitude at which space is said to begin, marking a huge leap in the firm’s space programme.
This was the plane’s fourth test flight, and marked a departure from previously unsuccessful attempts.
Sir Richard is in a race with Elon Musk and Jeff Bezos to send the first fee-paying passengers into space.
He is said to have shed a few tears and hugged his son as they watched the aircraft head off on its 90-minute journey.
The craft was manned by two pilots, Mark Stucky and Nasa astronaut Frederick Sturckow.
Speaking after take-off, the Virgin founder Sir Richard said: “I’m not supposed to say this, but hopefully we will go to space today.
“Hopefully we’ll have a bit of magic in the next couple of hours.”
In 2008, Virgin Galactic first promised sub-orbital spaceflight trips for tourists would be taking place “within 18 months”.
It has since regularly made similar promises to have space flights airborne in the near future.
But delays and a fatal crash in 2014 prevented Sir Richard’s original ambitions.
Today, however, Sir Richard has reason to celebrate.
The company said the space ship’s motor burned for 60 seconds, travelling at 2.9 times the speed of sound as it gained height.
The plane carried the two pilots and a mannequin named Annie as a stand-in passenger.
Before the flight, it said the aim of the plane, also known as the VSS Unity, would “aim to fly higher and faster”.
It planned to “burn the rocket motor for durations which will see our pilots and spaceship reach a space altitude for the first time”, it added.
However, it cautioned: “Although this could happen as soon as the next flight, the nature of flight test means that it may take us a little longer to get to that milestone.”