The rocket, which the space agency Nasa and Amazon founder Bezos expect to be able to take people to the moon in the future, lifted off from Cape Canaveral in Florida after a four-day wait due to bad weather.
Along for the ride are two NASA vehicles, which are headed for the planet Mars, where they are expected to arrive in 2027.
Cheers erupted in the control room as the launch vehicle, after separating from the upper part and the vehicles, landed on a barge out in the ocean. This means that, like competitor Elon Musk's SpaceX, the rocket can be reused and thereby reduce costs.
Next stop, the moon!, shouted employees at Bezos' space venture, which goes by the name Blue Origin.
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