The pair, who have remained anonymous since the announcement, will travel in an autonomous, unpiloted spacecraft in a lunar fly-by.
"I think they are entering this with their eyes open, knowing that there is some risk here," Musk told reporters in a telephone news conference in February.
"They're certainly not naive, and we'll do everything we can to minimise that risk, but it's not zero. But they're coming into this with their eyes open," said Musk, adding that the pair will receive "extensive" training before the flight.
While Musk's passengers remain a mystery, the renowned physicist Stephen Hawking will be among Virgin Galactic's first passengers.
Hawking said Branson offered him a seat which he accepted immediately.
It's estimated the cost of a trip on the SpaceX Dragon 2 to the moon would be roughly $100 million. A trip into sub-orbital space on the Virgin Galactic SpaceShipTwo comes in at a more reasonable $350,000.
The trip would also require nerves of steel after recent disasters.
A SpaceX rocket exploded during a test flight last September, though Musk believes passengers would have been able to escape.
Virgin Galactic was struck by tragedy in 2014 when a co-pilot was killed and another pilot seriously injured in a crash in the Mojave desert.