Blue Origin's massive BE-4 engine has been selected to power the joint Boeing and Lockheed Martin venture's Vulcan rocket, according to the report.
The first flight is scheduled for mid-2020.
Bezos' company has also been developing the liquid oxygen-powered BE-4 engine to power its own New Glenn rocket.
"Today is a great day for the Blue Origin team".
"Vulcan Centaur will revolutionize spaceflight and provide affordable, reliable access to space for our current and future customers", ULA chief executive Tory Bruno said in a release.
The Vulcan Centaur is now in the design phase, with the booster preliminary design and critical design reviews completed.
Following completion of a competitive procurement, ULA has selected Blue Origin's BE-4 engine for Vulcan Centaur's booster stage. A spokesman for Blue Origin did not immediately respond to requests for comment.
ULA's "Plan B" was to turn to Aerojet Rocketdyne's kerosene-fueled AR1 engine, but that engine was thought to be far behind the BE-4 on its development timeline.
"We are well on our way to the introduction of Vulcan Centaur - the future of USA rocket manufacturing", Bruno said. Huntsville led the USA propulsion revolution in the '60s, and we continue to do so with a thriving industry of rocket scientists and rocket producers.
Blue Origin's victory marks a "major defeat" for Aerojet because it essentially leaves the company out of the market for developing main engines for any of those heavy-lift launch vehicles, Ostrove said.
"The long-term vision is millions of people living and working in space".