The launch was carried out at 01:20 GMT on Sunday, from the Kennedy Space Center at Cape Canaveral, Florida, with a live podcast from SpaceX.
"Falcon 9's first stage has landed on the A Shortfall of Gravitas droneship - completing SpaceX's first 14th flight of a first stage booster," SpaceX said on social media about half an hour after the launch.
The Falcon 9 rocket carried 34 Starlink satellites and AST SpaceMobile's BlueWalker 3 satellite to orbit.
The Starlink project seeks to provide more affordable access to broadband internet connection across the world.