Leaked plans reveal that some employees will be paid off with nearly 15 months' salary and a cheque for £10,000.
Opposition parties yesterday raised fears that the job losses could harm the service.
The country's eight existing forces will make way in April for Police Scotland, the country's new single force headed by Chief Constable Stephen House.
Ministers backed the controversial policy on the grounds that a merger would bring efficiencies and save public money. However, the Scottish Government's policy of maintaining police officer 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.
So far, the controversy has centred around tensions between House and Vic Emery, who chairs the Scottish Police Authority (SPA), a body that will be the formal employer of staff.
The Sunday Herald can reveal that the Scottish Government has agreed in principle to a national redundancy scheme drawn up by the SPA. According to a leaked SPA paper, the deal has two elements.
For most employees in their 50s, an early retirement package will be available. The pay-off will include a lump sum capped at 30 weeks' salary, bolstered by up to four "added years" of pension payments.
Other staff will be offered redundancy, which will include a cash payment based on completed years of service. 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. This sum was agreed in a bid to attract younger staff with fewer years of service.
In Strathclyde, it is estimated that 57% of police staff have service of less than 10 years.
However, the £10,000 golden goodbye could have been more generous for some higher earners. According to the SPA, a proposal for a 25% boost on top of redundancy payments was floated but dropped.
The paper calculated the potential cost of the scheme on the basis of 1400 staff being released. In that case the package 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.
ASEPARATE SPA board paper makes it clear agreement has been reached on the national redundancy plan: "The Convenor [Emery] has now written formally to Scottish Government and formal approval by the Cabinet Secretary is expected within the next few days."
However, concerns are being expressed on the effect of the cuts.
An advantage of employing civilian staff is that it frees up police officers from desk-based jobs. Critics believe the same officers may now have to be used to "back-fill" the posts left by police staff.
Gerry Crawley, the lead negotiator for police support staff at the Unison union, said: "In our view there is no necessity for this level of redundancy. It will result in police officers covering support staff roles, a situation that is not best value and which will end up costing the taxpayer more. There needs to be a balanced workforce and the arbitrary target on maintaining police officer numbers needs to be closely examined by the new service and the Scottish Government."
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. All the gains of civilianisation of the last 15 years, freeing up police officers to do real police work, are being thrown away by this reckless and incompetent government."
Scottish LibDem MSP Alison McInnes said: "We've already seen a number of rounds of redundancy in the last few years, so the prospect of the loss of a further 1400 jobs is deeply worrying. One of the main concerns we had about the creation of a single police force is that it artificially simplifies a complex system. Whether out on the beat or providing technical expertise, every job is important in serving the needs of local communities."
An SPA spokesman said there was "no target" at the moment for the number of staff who may be accepted for voluntary redundancy, but financial modelling had been required in order to understand the potential impact of the scheme.
"This was provided by Police Scotland and includes an indication of what the costs associated with 1400 people look like. That was assessed as a sensible mid point between the best and the already much-publicised worst-case scenarios."
He added: "As with any voluntary scheme, the numbers of staff who take VR/ER (voluntary redundancy/early retirement) will be highly dependent on the number of people who come forward."
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