The idea was that the rocket would take off on Monday, but the launch was postponed due to technical problems.
The New Glenn rocket is part of Bezos' space venture Blue Origin. It is named after astronaut John Glenn, is 98 meters high and was launched from Cape Canaveral in the state of Florida.
Amazon founder Bezos was himself present in the control room during the launch on Thursday. He says he doesn't see Blue Origin as a competitor to Elon Musk's Space X.
There is room for many winners, he said over the weekend and added that this is the beginning of a new phase of the space age.
Blue Origin hopes for six to eight New Glenn launches during the year.
