“We’re finally able to open our doors to private citizens and allow others to experience the magic of living and working in space,” said Dana Weigel, deputy manager for the space station at NASA. “The dream is really to allow everyone access to space, and this is a pretty exciting starting point here.”

Producers of Discovery’s “Who Wants to Be an Astronaut” expect the winner to be on board for the second Axiom mission to the space station, which might take off six or seven months after the first one. For now, an agreement between the Discovery team and Axiom has not been finalized, and NASA has yet to choose Axiom to conduct the second private space tourism flight.

The NASA-led part of the station could accommodate two private astronaut missions a year, space agency officials have said, and other companies are also interested in participating.

“We are seeing a lot of interest in private astronaut missions, even outside of Axiom,” Ms. Weigel said. “At this point, the demand exceeds what we actually believe the opportunities on station will be.”

Still, on Tuesday, Axiom announced two people who would be in the seats for that second mission: Peggy Whitson, a former NASA astronaut who now works for Axiom, will be the commander, and John Shoffner, a paying passenger who made his fortune as head of a company that manufactures conduits for fiber optic cables, will serve as pilot for the mission.

Dr. Whitson, who holds the record for the most cumulative time in space by a NASA astronaut — 665 days — joined Axiom as a consultant a year ago, in hopes of getting to space again and adding to her record. “Yes, most definitely,” she said. “That was the carrot.”

Mr. Peterson said plans for the Discovery show grew out of discussions with Axiom early in 2020 and that it would be “a premium documentary” and less like “Survivor” or other ruthless reality television competitions.