The rocket lifted off on Sunday morning from Cape Canaveral, Florida, and the booster touchdown happened about 10 minutes later.
New Glenn carried AST SpaceMobile's BlueBird 7 satellite to low-earth orbit in a flight that marks a pivotal step for the company.
The mission was key to demonstrating that New Glenn, a 29-storey heavy-lift rocket, has a reliable booster reuse capability and can compete with Elon Musk's SpaceX Falcon 9 rocket.
The rocket's booster, dubbed "Never Tell Me the Odds," previously flew on the NG-2 mission in November and was recovered, setting up this week's milestone attempt.
The booster's name is a nod to a Han Solo line in the film Star Wars: The Empire Strikes Back.
New Glenn is designed for the higher end of the commercial launch market with a seven-metre nose cone allowing it to carry bulkier payloads, including multiple satellites in a single mission.
AST SpaceMobile's BlueBird 7, carried into orbit on NG-3, is the second satellite in its next-generation Block 2 constellation.
The satellite features what the company describes as the largest commercial communications array deployed in low-earth orbit.
Designed to connect directly with smartphones, the satellite is part of an effort to build a space-based mobile phone broadband network, similar to Amazon's Leo or SpaceX's Starlink.
AST SpaceMobile is targeting a constellation of 45 to 60 such satellites by the end of 2026.
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