Blue Origin LLC, the space-transportation company run by Jeff Bezos, has won a contract to provide engines for a potential rival’s next-generation rocket, further roiling a tumultuous industry and vaulting Mr. Bezos into the lucrative market for Pentagon satellite launches.

United Launch Alliance LLC—a joint venture between Boeing Co. and Lockheed Martin Corp. that launches U.S. military and spy satellites into orbit—on Thursday announced that after a lengthy competition, it picked Blue Origin’s BE-4 engine for its Vulcan rocket. “Our new rocket will be superior in reliability, cost and capability,” Tory Bruno, ULA’s president and chief executive, said in a press release, adding that “our certification plan is in place” with the first flight scheduled for mid-2020

The long-term, potentially multibillion-dollar agreement could provide a boost to Blue Origin’s eventual goal of becoming a major military launch provider itself. The company plans to use the same engines to power its own heavy-lift launcher, called New Glenn, which is under development. The announcement didn’t provide details about prices or other specifics.

Many industry experts expect that the development deadline is likely to be extended, with regular operations of the Vulcan booster potentially starting before the middle of the next decade. Even if everything goes smoothly, testing and final certification of the New Glenn booster is also expected to take roughly that long.

The Blue Origin engines have strategic importance for the Pentagon because they are intended to end the use of Russian-built RD-180 engines, which now provide primary propulsion on United Launch’s workhorse Atlas V rockets.