Identities of the two citizens haven't been revealed, but SpaceX said they "have already paid a significant deposit to do a moon mission."
The mission will use one of SpaceX's Dragon 2 capsules to house the crew, which will be carried by a SpaceX Falcon Heavy rocket that will launch for the first time this summer. It will lift-off from Kennedy Space Center's historic Pad 39A near Cape Canaveral.
SpaceX will conduct health and fitness tests, as well as begin initial training for the private citizens later this year.
Before SpaceX flies the space tourists in the Dragon 2, it will first send a NASA crew to the International Space Station. This first demonstration mission will be in automatic mode, without people on board. A subsequent mission with crew is expected to fly in the second quarter of 2018.
"NASA always has first priority," Elon Musk, CEO of SpaceX, said. "If NASA decides to have the first mission of this nature be a NASA mission, then of course NASA would take priority."
Private missions could drive significant revenue to SpaceX, Musk told reporters, speculating an increase of 10 to 20 percent. "There is likely a market for at least one or two of these per year," Musk said.
SpaceX successfully lands rocket in middle of ocean