Key civilian staff will be axed as part of the merger of the country's eight existing police forces.
Some will leave with nearly 15 months' salary and a cheque for £10,000.
Ministers backed the merger of the eight existing police forces on the grounds that it would save money.
However, the Scottish Government's policy of maintaining police numbers means a big chunk of the savings will come from getting rid of civilian staff.
These employees perform vital support services, including control room functions, forensics and fingerprints.
The Scottish Government has agreed in principle to a national redundancy scheme drawn up by the Scottish Police Authority.
For most employees in their 50s, an early retirement package will be available.
Other staff will be offered redundancy. At the top end of the scale, a 50-year-old with 20 years' service will get 66 weeks of pay.
Staff who take redundancy will also get a £10,000 sweetener on top of their deal.
The paper calculated the potential cost of the scheme on the basis of 1400 staff being released. That would cost the taxpayer £61.3m, most of which would be funded by the Scottish Government.
The annual saving from such a staff cull would be £39.8m.
Lewis Macdonald, Scottish Labour's justice spokesman, said: "The single police force was supposed to bring savings that would help protect frontline services.
"Instead, we have tens of millions of pounds spent on getting civilian staff out of the service so cops can be taken off the frontline to do civilian jobs."