Blue Origin conducted the test on Monday in West Texas but released the video Tuesday morning.
The company said the rocket, with a crew capsule, reached a height of 62 miles, and in just a few minutes, the capsule made a controlled vertical landing from where it took off.
The test proved the possibility of reusing rockets, which could save commercial aeronautics a lot of money.
Musk tweeted Bezos and the Blue Origin team for achieving take-off and landing on their booster.
Congrats to Jeff Bezos and the BO team for achieving VTOL on their booster— Elon Musk (@elonmusk) November 24, 2015
However, the SpaceX owner also took a dig at Bezos to clear up the difference between space and orbit.