He was accompanied by Mark Bezos, his brother, Wally Funk, an 82-year-old pioneer of the space race, and an 18-year-old student.
They travelled in a capsule with the biggest windows flown in space, offering stunning views of the Earth.
All four passengers have now parachuted safely back to Earth after their 11-minute trip.
New Shepard, built by Bezos’ company Blue Origin, is designed to serve the burgeoning market for space tourism.
The passengers included the oldest person who has been to space – Ms. Funk – and the youngest, student Oliver Daemen.
The spacecraft lifted off at 14:12 BST (09:12 EDT) from a private launch site near Van Horn, Texas.
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After the capsule touched down, Bezos said: “Astronaut Bezos [his callsign]: Best day ever!”
Two minutes into the flight, the capsule separated from its rocket and continued upwards towards the Karman Line – the most widely recognized boundary of space, 100km up.