Maezawa also said he would invite six to eight artists from around the world to join him on the trip as a creative project.
The ride will take place aboard a Big Falcon Rocket (BFR), which may not be ready for human flight for five years at least, Musk said.
SpaceX, which has received billions in NASA funding for parts of their development, hopes to be the first private company to send astronauts to the space station.
Instead, Musk's firm promised to announce the identity of the soon-to-be-astronaut on Monday, September 17. A total of 24 NASA astronauts - all white men - voyaged to the Moon during the Apollo era of the 1960s and '70s.
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The space company has already started serious development of the BFR. A rendering released with the company's tweet last week showed the rocket passing by the moon.
The businessman will not land on the moon itself, but will travel on what is known as a "free return trajectory", in a loop of sorts. That Christmas Eve, the crew famously read from the book of Genesis as they passed 60 miles above he lunar surface.
Maezawa, 42, will be the first lunar traveler since the last US Apollo mission in 1972.
Will they be landing on the Moon?
Inc. Chief Executive Jeff Bezos' Blue Origin has announced a lunar cargo delivery service called Blue Moon, which a company executive said could be functional in the next 5 years and capable of delivering large payloads. The space agency also aims to build a staffed gateway near the moon during the 2020s.
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The company first promoted the idea of a privately-funded lunar flight in an announcement on February 17, 2017. Rest assured Maezawa, I won't say no. "And they're very serious about it". The BFR will be the successor to SpaceX's oft-used Falcon 9 rocket and its upgraded version, the Falcon Heavy.
Musk later reversed course, saying the company no longer has plans to certify the Falcon Heavy for human spaceflight.
The mission is set to launch as soon as 2023, though Musk said he couldn't be sure about that timeline yet.
Though SpaceX and its chief executive, Elon Musk, have always been focused on Mars colonization, a moon mission could help "keep the momentum alive" and attract more private investment, said Marco Caceres, senior space analyst at Teal Group.
SpaceX calls the rocket the BFR, which officially stand for Big Falcon Rocket, though the F in the name is more commonly thought to stand for something else.
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