The four guests will spend just over a week there, before returning to Earth in their capsule.
The 270-mile-high (430-kilometer-high) docking puts the space station population at 11, representing not only Saudi Arabia and the U.S., but the United Arab Emirates and Russia.
Saudi Arabia’s government is picking up the multimillion-dollar tab for its first female astronaut, Rayyanah Barnawi, a stem cell researcher, and fighter pilot Ali al-Qarni.
John Shoffner, a Knoxville, Tennessee, businessman who started a car racing team, is paying his own way.
Retired NASA astronaut Peggy Whitson is their chaperone.
She now works for Axiom Space, the Houston company that organised the 10-day trip, its second to the space station. The company cited ticket prices of $55 million each for last year’s private trip by three businessmen, but won’t say how much the latest seats cost.
Only one other Saudi has flown before in space, a prince who rode on NASA’s shuttle Discovery in 1985.
Watch: SpaceX sends Saudi astronauts to International Space Station
Saudi Arabia’s first astronauts in decades rocketed toward the International Space Station on a chartered multimillion-dollar flight Sunday. SpaceX launched the ticket-holding crew, led by a retired NASA astronaut now working for the company that arranged the trip. Also on board: a U.S. businessman who now owns a sports car racing team.