The mission "will provide up to four individuals with the opportunity to break the world altitude record for private citizen spaceflight and see planet Earth the way no one has since the Gemini program," Space Adventures said in a statement, referring to the 1960's NASA program.
This mission will also "be the first orbital space tourism experience provided entirely with American technology," the company added.
The private astronauts will fly on SpaceX's Crew Dragon spacecraft using the Falcon 9 rocket. This is the same combination that is slated to transport NASA astronauts to the International Space Station as part of NASA's Commercial Crew program.
The Falcon 9 recently underwent a successful safety test.
Gwynne Shotwell, the president and COO of SpaceX, said the mission "will forge a path to making spaceflight possible for all people who dream of it," in a statement Tuesday.
Eric Anderson, the chairman of Space Adventures added that the company exists to create "unique and previously impossible opportunities for private citizens to experience space."
Their joint Dragon mission will be able to to reach "twice the altitude of any prior civilian astronaut mission or space station visitor," he said.
An exact timeline for the mission has not yet been released, but it could be as early as late 2021. The price of a ticket on the spacecraft was not disclosed.
Japanese billionaire Yusaku Maezawa has famously paid his way to become the first private passenger to visit the moon with SpaceX, also for an undisclosed amount of money. Some estimate that Maezawa, who recently gave away $9 million on Twitter, paid millions for his SpaceX ticket.