Branson said more than 7,000 people had registered their willingness to pay the $210,000 fare for the service, which promises to send passengers 70 miles above the Earth.
Speaking from California's Mojave desert, Branson told Britain's Press Association news agency there had been "tremendous take-up" of the idea since he announced it last month.
"We are extremely pleased because it just means in a sense that the gamble we took seems to have paid off," he said.
Branson, 54, said he had committed $110 million toward spaceships and ground infrastructure for the new service, Virgin Galactic. He also plans to spend up to $26 million to license the technology of SpaceShipOne, the rocket-plane that made two successful suborbital space flights earlier this month to capture the $10 million Ansari X Prize.
Virgin hoped to offer flights — lasting about 3 1/2 hours including six minutes of weightlessness — by 2008.
Branson said he would go on the first flight, along with family members including his father, now 86.
"My dad has put his hand up and will be 90 at the time, my kids definitely want to come and if there is room for my mum she will come as well," Branson told PA.
But he said his wife Joan "will have her feet firmly on the ground, I suspect, trying to encourage the kids to stay on the ground."
Branson is one of Britain's best known and most colorful entrepreneurs. His Virgin Group began as a record label, and now sells everything from soft drinks to bridal gowns, and even runs a train service and mobile phone network.