The two companies combined their controls businesses in 2009 to form Aero Engine Controls. The joint venture employs about 1,400 people in Birmingham, Derby and Belfast in Britain and in Indianapolis in the United States.
"Engine control systems play an increasingly important part in enhancing the fuel efficiency and overall performance of modern jet engines," Rolls-Royce said on Friday.
"This acquisition will give Rolls-Royce full ownership of a critical capability that confers competitive advantage."
Rolls-Royce said the deal had been agreed with United Technologies Corp, which is in the process of buying aircraft components maker Goodrich.
The British company said it would pay half of the net asset value of AEC once the takeover had completed.
The joint venture, which was designed to break even, had gross assets of £116m at the end of 2011 and net assets of £8m, along with debt of about £54m, Rolls-Royce said in a statement