It took off from the Kennedy Space Center in Florida's Cape Canaveral just before sunset and then roared up into darkness.
Onboard was billionaire e-commerce executive, Jared Isaacman, alongside three crewmates and no professional astronauts.
They were strapped into the rocket's capsule, dubbed Resilience, wearing helmeted black-and-white flight suits.
And a thumbs up signalled they'd entered orbit almost 10 minutes after blastoff.
Cheers erupted in SpaceX's mission-control center.
The mission aims for a maximum orbit of nearly 400 miles above Earth.
That's higher than both the International Space Station and Hubble Space Telescope.
It's also the furthest any human has flown since NASA's 1972 Apollo moon mission.
The flight is expected to last about three days.
mission officials say it will then splash down in the Atlantic.
The launch marks the debut of SpaceX owner Elon Musk's orbital tourism business embraced by NASA.
Before Wednesday's launch, the space agency tweeted, "#Inspiration4 embodies our vision for a future in which private companies can transport cargo and people to low-Earth orbit. More opportunities to fly = more opportunities for science."
Time magazine has estimated Isaacman's four tickets cost $200 million.
