The world's second-largest aero-engine manufacturer will pay Cooper Cameron Corporation $180m (pounds 112m) for the stake, and Rolls-Royce will relocate its global energy business headquarters to Ohio as part of the deal.
The move was welcomed by the City, with Rolls-Royce shares rising by as much as 15p before settling back to 261.25p, down 1.25p on the day, amid City caution ahead of the company's first-half results next week.
The deal could lead to job losses at Rolls-Royce's Liverpool factory, which makes compression equipment for the oil and gas industries, and employs 174 people.
A spokesman for Rolls-Royce said that a "complete review of the business" would follow the completion of the acquisition. He refused to rule out job losses.
"It is too early to say what the impact of this deal will be, but people's jobs will be affected," the spokesman said.
Rolls-Royce shares have been gaining in recent days as sentiment has improved ahead of its results next week, with analysts predicting pre- tax profits of pounds 165m compared with pounds 135m for the same period last year.
Earlier this summer, General Electric beat Rolls-Royce to win a crucial engine supply contract for the long-range version of the Boeing 777 airliner, casting doubt on Rolls-Royce's ability to continue delivering double- digit earnings growth.Reuse content