The majority of cuts will be made in the UK, where it has 26,000 employees from a global total of 55,000.
In a statement, the engineering company said around 1,500 jobs would be lost by the end of this year alone.
The cuts and overhaul of its business will cost it £500 million and will be reported as one-off costs, enabling it stick to its targets for free cash flow.
Rolls Royce Chief Executive Warren East said: “We have made progress in improving our day-to-day operations and strengthening our leadership, and are now turning to reduce the complexity that often slows us down and leads to duplication of effort.
“It is never an easy decision to reduce our workforce, but we must create a commercial organisation that is as world-leading as our technologies. To do this we are fundamentally changing how we work.
“These changes will help us deliver over the mid and longer-term a level of free cash flow well beyond our near-term ambition of around £1 billion by around 2020.”
Unite Assistant General Secretary Steve Turner warned that Rolls-Royce is overdoing the overhaul of its business, which could “ultimately damage the smooth running of the company”.
He said: “This announcement will be deeply unsettling for Rolls-Royce workers and their families and could have a dire economic impact on local communities reliant on Roll-Royce jobs.
“There is a real danger that Rolls-Royce will cut too deep and too fast with these jobs cuts, which could ultimately damage the smooth running of the company and see vital skills and experience lost.
“Unite will be offering our members maximum support through this process and seeking assurances on no compulsory redundancies from Rolls-Royce for Unite members affected by this announcement.”
Previous job cuts under Mr East, who joined in 2015, have have seen 600 managers leave the business.
But this is the largest reduction in headcount since 2001, when the company announced plans to reduce 5,000 jobs, plus 1,000 contractors, which at the time was around 12 percent of its workforce.
The upheaval of the business comes at a time when Rolls-Royce is under increasing pressure in the biggest part of its business, its aero engines unit, after issues on some of its engines grounded planes and led to complaints from airline customers.
Problems with its newest engine, the Trent 1000, were first identified two years ago, with parts of the engine used on Boeing’s 787 Dreamliners wearing out faster than expected.
It started an inspection and modification programme but earlier this week it discovered new problems with the troubled engines, truggering fresh safety fears and potential disruption for airlines including British Airways and Norwegian.
In March, Roll-Royce signalled further job cuts amid plans to slash costs “significantly” after it bounced back from record losses with a £4.9 billion annual profit haul.
The group confirmed it had hired advisers Alvarez & Marsal to help it move to a “considerably” simplified staff structure as part of the wide-ranging restructure announced in January, sparking fears over fresh management job cuts.
It made the comments after revealling a pre-tax profit of £2.6 billion compared to when it fell into the red by £4.6 billion in 2016 in what was its largest ever loss and one of the biggest in UK crporate history.