Tony Wood, the head of aerospace, will depart, and Lawrie Haynes, who runs the land and sea division, will step down next year.
The change in structure is part of a plan to save up to £200m a year from 2017, it said.
Removing the top layer of management is a bid to simplify decision-making.
Rolls-Royce has issued a series of profit warnings that have battered its share price, leaving it down 38% this year.
