WASHINGTON — Jeff Bezos, the billionaire chief executive of Amazon, founded a rocket company as a hobby 16 years ago. Now that company, Blue Origin, finally has its first paying customer as it ramps up to become a full-fledged business.

Mr. Bezos announced that customer, the satellite television provider Eutelsat, on Tuesday. In about five years, Eutelsat, which is based in Paris, will strap one of its satellites to a new Blue Origin rocket to be delivered to space, a process it has done dozens of times with other space partners.

For Blue Origin, the relationship represents its evolution from an engineering-obsessed company into one that also seeks to make a profit eventually.

That goal may be a moon shot, with high risks, high costs and no guarantee that enough customers need transportation beyond Earth. Blue Origin, based in Kent, Wash., has launched only its New Shepard rocket to the edge of space, 62 miles up, before returning to Earth.