The company's shares surged as much as 40% to $56.40, their highest since February, after more than doubling in value this year.
The approval from the Federal Aviation Administration (FAA) comes at a critical time for Branson as his space venture faces off against Amazon.com founder Jeff Bezos' Blue Origin and Tesla Inc boss Elon Musk's SpaceX.
Bezos, Branson and Musk have been investing billions of dollars on their rocket startups.
Branson, who is reportedly flying to space himself in a bid to beat rival billionaire Bezos to the final frontier, received the green light just a month after a successful test flight.
Virgin Galactic last month completed its first manned space flight from its new home port in New Mexico in May, as its SpaceShipTwo craft with a capacity of six passengers glided to a landing on a runway safely with its two pilots.
The company has said it has more than 600 reservations for 90-minute flights that include several minutes of weightlessness, priced at $250,000 a ticket.
"Today's approval by the FAA ... gives us confidence as we proceed toward our first fully crewed test flight this summer," Virgin Galactic Chief Executive Officer Michael Colglazier said in a statement.
As of Friday afternoon, the company's stock was on track to post its biggest one-day gain in nearly five months.
(Reporting by Ankit Ajmera in Bengaluru; Editing by Devika Syamnath)