Elon Musk on Monday evening introduced Yusaku Maezawa, founder of the online Japanese clothing company Zozo, as his first customer for a voyage around the moon aboard a SpaceX rocket.

“Finally, I can tell you that I choose to go the moon,” Mr. Maezawa shouted.

Mr. Maezawa’s intent to follow in the contrails of American astronauts, who first looped the moon in 1968 aboard the Apollo 8 mission, was announced at an event at the company’s headquarters in the Los Angeles area. The expensive trip would cost at least tens of millions of dollars, if not a couple of hundred million, and when it would occur was not yet announced. Neither Mr. Musk nor Mr. Maezawa would disclose the price.

Mr. Maezawa is to ride a yet-to-be-built rocket known as the B.F.R. on a journey that would take four to five days. The rocket would not be ready for the trip until 2023, Mr. Musk said, and would cost from $2 billion to $10 billion to develop. He added that Mr. Maezawa’s ticket would make a meaningful contribution to the project’s completion.