Rayyanah Barnawi, a stem cell researcher, was joined by Ali al-Qarni, a fighter pilot with the Royal Saudi Air Force on the flight, which was sponsored by the Saudi Arabian government.
The pair are the first from their country to ride a rocket since a Saudi prince launched aboard the shuttle Discovery in 1985.
They will be greeted at the station by an astronaut from the United Arab Emirates.
“Hello from outer space! It feels amazing to be viewing Earth from this capsule,” Barnawi said after settling into orbit.
Al-Qarni added: “As I look outside into space, I can’t help but think this is just the beginning of a great journey for all of us.”
The rest of the crew was made up of John Shoffner, former driver and owner of a sports car racing team that competes in Europe, and chaperone Peggy Whitson, the station’s first female commander who holds the US record for most accumulated time in space: 665 days and counting.
“It was a phenomenal ride,” Whitson said after reaching orbit, while her crewmates clapped their hands in joy.
It marks the second private flight to the space station organised by Houston-based Axiom Space – the first took place last year by three businessmen, along with another retired NASA astronaut.
The company plans to start adding its own rooms to the station in another few years’ time, eventually removing them to form a stand-alone outpost available for hire.
Axiom won’t say how much Shoffner and Saudi Arabia are paying for the planned 10-day mission. The company had previously cited a ticket price of $55 million each.
NASA’s latest price list shows per-person, per-day charges of $2,000 for food and up to $1,500 for sleeping bags and other gear.
SpaceX’s first-stage booster landed back at Cape Canaveral eight minutes after liftoff – a special treat for the launch day crowd, which included about 60 Saudis. “It was a very, very exciting day,” said Axiom’s Matt Ondler.
The four should reach the space station in their capsule Monday morning; they will spend just over a week there before returning home with a splashdown off the Florida coast.