Middle managers and back-office staff are to bear the brunt of the cuts, which are expected to hit its Derby base hard.
The company is refocusing its business on civil aerospace, defence and power systems.
About a third of the job cuts are expected to happen by the end of this year, Rolls-Royce said.
The programme is expected to continue throughout 2019, with full implementation by mid-2020.
Rolls-Royce said that the programme would cost £500m to carry out, including redundancies, but would save it £400m a year by the end of 2020.
The firm also said it would continue to work on its problems with its Trent 1000 engine.
Parts in the engines have been wearing out faster than anticipated, causing some planes to be grounded. Rolls-Royce has said it will take years to modify all the engines in service.