The price tag for Maezawa's ticket isn't clear and SpaceX did not make that information public. He will bring six to eight artists with him, he said.
The mission in question is planned for 2023 and would be the first lunar journey undertaken by humans since 1972, when the final Apollo mission took place.
The Big Falcon Rocket is scheduled to make the trip in 2023, SpaceX founder Elon Musk announced at an event Monday at its headquarters near Los Angeles.More news: Firmino strikes late to give Liverpool victory
In February 2017, SpaceX said two "private citizens" had "paid a significant deposit" for a trip around the moon. That mission was to use SpaceX's Dragon crew capsule and Falcon Heavy rocket.
Musk introduced Yusaku Maezawa, founder of the global custom-fit clothing company Zozo and an avid art collector, as the one who is investing in the spaceship project in order to take the trip, possibly in 2023.
Forbes ranks Maezawa as the 18th richest person in Japan.
The trip will be expensive. Musk did not name the clients previous year or say how much they would pay.
Hasn't this space trip to the moon been promised before?You have to be pretty loaded to score a tourist spot on a spaceship. More news: Drake files extortion lawsuit accusing Instagram model of faking pregnancy, rape allegations
Russian and Chinese companies are also working on space tourism plans.
Musk and other private spaceflight CEOs have been striving to fill that gap with spacecraft that can get crews to the ISS and beyond.
He will become the first non-American to orbit the moon. The moon's orbit is, on average, 238,855 miles (384,400 km) away. The plan is to send passengers around the moon and back - a more than 475,000-mile journey - in about five days.
After people responded with questions, Musk weighed in and confirmed that the render of the Big Falcon Rocket, which is still in development, is new and "intentionally" created to resemble one seen in a classic Tintin comic.
It'll have forward actuated fins, and rear actuated fins, and it'll be powered by SpaceX's Raptor thrust engine.
Mr Musk added: "We will carry out many test flights before we put any people on board". Musk said Maezawa's payment is big enough to "have a material effect on paying for cost and development of BFR", which could cost as much as $5 billion overall.More news: Accuser of Trump's Supreme Court pick seeks Federal Bureau of Investigation probe