The capsule is to launch atop SpaceX's Falcon Heavy rocket, which is set to have its first flight this summer. While SpaceX did not say how much the individuals paid for the mission, the price is comparable to what a crewed mission to the International Space Station would be.
Once the Dragon crew missions get underway, SpaceX will launch the private moon mission later in the year.
Musk says SpaceX is on track to launch astronauts to the International Space Station for NASA in mid-2018.
During a conference call with reporters, he said the two individuals know each other.
SpaceX founder Elon Musk said the mission would take approximately a week.
Worth noting: they won't be landing on the moon - they're going to blast around it and return back to earth. This will be the first crewed spaceflight for the Dragon.
SpaceX has already been developing the Crew Dragon to carry people for NASA, as part of the agency's Commercial Crew Program. This first demonstration mission will be in automatic mode, without people on board.
SpaceX said Dragon spacecraft has been created to carry humans from the beginning.
"NASA always has first priority", Musk said, "so if NASA decides to have the first mission of this nature be a NASA mission, then of course NASA would take priority". These missions will build upon that heritage, extending it to deep space mission operations, an important milestone as we work towards our ultimate goal of transporting humans to Mars.