As Reuters reports, the actual cost of the trip hasn't been revealed, but Maezawa noted that the journey will set him back significantly more than his art purchases.
"Finally, I can tell you that I choose to go to the Moon!" the Japanese entrepreneur proclaimed.
According to Forbes, Maezawa is worth $2.9 billion. The Japanese billionaire is the founder and CEO of Japanese fashion retailer Zozo.
The moon hasn't seen any human visitors since 1972 and NASA's last Apollo mission.
Mr Maezawa did not immediately say who will be on his guest list for the spaceflight, but in response to a question from a reporter he said he would consider inviting Mr Musk. While the spacecraft has yet to be fully developed or flight tested, the company says the next generation BFR "will be the most powerful rocket in history", able to "carry humans to the Moon, Mars, and beyond". The mission is now scheduled for 2023, so Maezawa will have some time to gather his dream team.
Mr Maezawa then explained he had hired the entire shuttle, not just one seat, adding that he wanted to be joined by several artists. Sixteen successful missions for SpaceX this year is a bright spot in an otherwise tumultuous few months for Musk, who is also chairman and chief executive officer of electric-car maker Tesla Inc.
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During the same press conference, Musk unveiled an updated design for the BFR rocket; it now stands at 118 meters, making it taller than the original Apollo mission rockets, which sent the first astronauts to the Moon.
"He's paying a lot of money that would help with the ship and its booster", Musk said on Monday.
The company is still developing the BFR rocket, which will be the successor to SpaceX's oft-used Falcon 9 rocket and its upgraded version, the Falcon Heavy.
The trip is expected to take several days, and is slated for 2023.
The rocket dubbed BFR has not been built so any flight is several years away.