The stubby white spacecraft with a round tip blasted off into clear blue skies over West Texas for a trip of about 11 minutes to slightly beyond the internationally recognised boundary of space, 100 kilometres high.
The six-member crew shouted with glee as they unbuckled to enjoy a few minutes of weightlessness, looking out at space through tall windows in the capsule.
“I have never seen anything like that,” one crew member said in audio captured during the live-streaming of the flight by Blue Origin.
The capsule quickly returned to Earth for a gentle parachute landing in the desert, kicking up a cloud of dust as it touched down.
Mr Bezos and other company officials rushed to greet the crew members as they emerged smiling from the capsule. The booster rocket touched down separately and also safely.
“We had a great flight today,” Blue Origin chief executive Bob Smith said.
Laura Shepard Churchley, whose father Alan Shepard became the first American to travel to space in 1961, flew as a guest of Blue Origin.
The company's suborbital rocket is named New Shepard in honour of the pioneering astronaut.
Michael Strahan, an American football Hall of Famer turned TV personality, was also a guest, while there were four paying customers: space industry executive and philanthropist Dylan Taylor, investor Evan Dick, Bess Ventures founder Lane Bess and his son Cameron.
Lane and Cameron became the first parent and child to fly together to space. The cost of tickets on the suborbital flight were not disclosed.
Alan Shepard made US history with a 15-minute suborbital space flight on May 5, 1961, slightly under a month after the Soviet Union's Yuri Gagarin became the first person in space when he orbited the planet.
Mr Shepard, who died in 1998, went on to be the fifth of 12 men to have set foot on the Moon.
“It is kind of fun for me to say an original Shepard will fly on the New Shepard,” Ms Shepard Churchley, who runs a foundation that promotes science and raises funds for college students, said in a video before the flight. “I am very proud of my father's legacy.”
Previous Blue Origin flights took the company's billionaire founder Jeff Bezos and Star Trek actor William Shatner to space.
Mr Bezos, who made his fortune with Amazon, envisages a future in which humanity disperses throughout the solar system, living and working in giant space colonies with artificial gravity.
This, he says, would leave Earth as a pristine tourism destination similar to national parks today.
The year 2021 has been significant for the space tourism sector, with Virgin Galactic also flying its founder Richard Branson to the final frontier and Elon Musk's SpaceX sending four private citizens on a three-day orbital mission for charity.