If you have tens of millions of dollars to spare, you could as soon as next year be one of three passengers setting off aboard a spaceship to the International Space Station for a 10-day stay.

On Thursday, Axiom Space, a company run by a former manager of NASA’s part of the space station, announced that it had signed a contract with SpaceX, Elon Musk’s rocket company, for what might be the first fully private human spaceflight to orbit.

“I think you’ll see a lot more energy in the market as people come to realize it’s real, and it’s happening,” said Michael T. Suffredini, the president and chief executive of Axiom.

The spaceflight, Axiom officials said, could take off as soon as the second half of 2021.

SpaceX developed its Crew Dragon capsule for taking NASA astronauts to and from the space station. But just as the company’s development of its Falcon 9 rocket for taking cargo to the space station led to a vibrant business of launching commercial satellites, SpaceX is also looking to expand Crew Dragon passengers beyond just NASA astronauts.