“Congratulations on getting into orbit on your first try!” Musk wrote in a message to Bezos on X.
Dave Limp, CEO of Bezos’ space company Blue Origin, said he was “incredibly proud”.
“We’ll learn a lot today and try again at the next launch this spring,” he added.
Bezos’ team overcame technical hurdles that caused delays earlier this week when an ice formation halted the launch.
Blue Origin employees and crowds gathered near Cape Canaveral cheered as the 98-meter-tall rocket blasted into orbit.
But the company failed to land the New Glenn rocket’s main engine or launch vehicle on the platform in the Atlantic Ocean.
The company hoped the launch vehicle could be used for future launches, but about 20 minutes into the flight, the company confirmed it had lost an engine.
Bezos’ company, Blue Origin, has struggled to match the pace set by SpaceX. But this launch will be seen as an important step forward for the business.
The New Glenn rocket was named after John Glenn, the first American astronaut to orbit the Earth more than 60 years ago.
The rocket is more powerful than SpaceX’s most commonly used rocket, the Falcon 9. It can also carry more satellites, and Bezos wants to use it as part of his Kuiper project, which aims to deploy thousands of low-Earth satellites to provide broadband services. .
This project will directly compete with Musk’s Starlink service.