The space plane detached from the mother ship at an altitude of about 8 miles (13 kilometers) and fired its engine. It reached the edge of space at about 53 miles (88 kilometers) up.
The crew successfully landed after an hour-long trip.
Who flew with Branson?
Branson was joined by two pilots, Dave Mackay and Michael Masucci, as well as Beth Moses, Virgin Galactic's chief astronaut instructor, lead operations engineer Colin Bennett, and Sirisha Bandla, a research operations and government affairs vice president.
"Welcome to the dawn of a new space age," Branson said on Twitter, with a photo from inside his space ship.
In a short video released on Twitter prior to the flight, Branson said his goal was "to turn the dream of space travel into a reality — for my grandchildren, for your grandchildren, for everyone."
My mission statement is to turn the dream of space travel into a reality - for my grandchildren, for your grandchildren, for everyone.
Branson told crowds at the launchpad after his trip that after 17 years of work he finally got to enjoy testing "the customer experience." His company plans to start commercial operations next year.
Billionaires' space race?
The 70-year-old entrepreneur behind Virgin Atlantic and Virgin Records has beaten Amazon founder Jeff Bezos in the ultimate space race between some of the world's richest men.
Bezos plans to travel on July 20 on his own New Shepard suborbital rocketship built by his Blue Origin firm. The Amazon founder is set to pilot the spacecraft himself.
Tesla CEO Elon Musk also has ambitions to travel to outer space and eventually Mars, although his timetable is less clear. However, Musk's SpaceX project is expected to carry civilians into space as early as September this year.
Hours before the launch, Branson tweeted a photo of him with Musk. "Big day ahead. Great to start the morning with a friend," Branson said.
Big day ahead. Great to start the morning with a friend. Feeling good, feeling excited, feeling ready.
Ahead of the flight, Bezos' Blue Origin company pointedly noted that Branson was not even set to cross what most countries see as the border of outer space.
But Bezos himself wished Branson "a successful and safe flight" on Instagram.
Branson's VSS Unity climbed to over 80 kilometers, which the US Air Force and NASA consider to be the boundary between the Earth's atmosphere and outer space. But the World Air Sports Federation, known by its French acronym FAI, is the world governing body for air sports and defines human spaceflight differently.
The Lausanne-based organization defines outer space as 100 kilometers above Earth's mean sea level, the so-called Karman Line, 12 kilometers higher than Branson is going to travel.
Blue Origin CEO Bob Smith dismissed Virgin Galactic’s approach as "a very different experience" because "they’re not flying above the Karman line."
Only 4% of the world recognizes a lower limit of 80 km or 50 miles as the beginning of space. New Shepard flies above both boundaries. One of the many benefits of flying with Blue Origin. pic.twitter.com/4EAzMfCmYT
That controversy has not dissuaded people from snapping up tickets for the first space tourism flights.
Leonardo DiCaprio and Justin Bieber are among the 600 customers to have stumped up for the $250,000 (€210,000) seats.
Branson founded Virgin Galactic 17 years ago, with it now attempting to finish development testing this year so it can begin flying space tourism passengers in early 2022.
He, Musk and Bezos have pumped billions into their respective projects, but this could prove to be a canny investment.
Switzerland's UBS predicts the value of the space tourism market will hit $3 billion annually by 2030.
