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.
When the capsule touched back down after the 10-minute, 10-second flight, Jeff Bezos exclaimed: "Best day ever!"
New Shepard, built by Bezos' company Blue Origin, is designed to serve the burgeoning market for space tourism.
Amazon founder Mr Bezos - and other participants in the "billionaire space race" - have been criticised for offering what some see as joy rides for the super-wealthy. Critics say the money could be spent on pay rises for employees or fighting climate change.
However, Mr Bezos insists he has an environmental vision: "We need to take all heavy industry, all polluting industry and move it into space, and keep Earth as this beautiful gem of a planet that it is," he told MSNBC.
"It's going to take decades and decades to achieve, but you have to start, and big things start with small steps... that's what this sub-orbital tourism mission allows us to do, it allows us to practice over and over."
The spacecraft lifted off at 14:12 BST (09:12 EDT) from a private launch site near Van Horn, Texas.
At a post-launch news briefing, Jeff Bezos said: "My expectations were high and they were dramatically exceeded."
Two minutes into the flight, the capsule separated from its rocket and continued upwards towards the Karman Line - the most widely recognised boundary of space, that lies 100km up. The newly minted-astronauts shouted "wow!" and cheered.