Forty-five teaching staff have successfully applied to the scheme, while 44 "professional service staff" – which includes employees from student affairs, human resources and IT – are also leaving the university.
A total of 116 applications for voluntary severance were made by employees, after the university opened the offer to all staff last summer.
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Hide AdAn e-mail was sent to staff last week informing them of the final outcome of the voluntary severance scheme.
The university says it needed to introduce the scheme to meet its "future academic and business needs" and offered the voluntary severance scheme to all staff in order to try and prevent compulsory redundancies.
University bosses initially estimated that 60 jobs would be made redundant.
An Edinburgh Napier University spokesman said: "Like many other successful academic institutions we operate a voluntary severance scheme to help ensure that we have a sustainable number of staff to meet our future academic and business needs.
"Some staff have already left the university and others will be leaving over the next few months.
"We would like to thank all staff for their contributions to Edinburgh Napier University and to wish them all the best for their future."
Edinburgh University is also preparing to have to make staff redundant. It emerged last month that universities across Scotland could be forced to make up to 100 staff redundant, or even close entire departments, due to cuts in teacher-training places.
Lecturers' union the UCU claimed in a report that a move by the Scottish Government to reduce the number of new teachers produced in Scotland will have a major financial effect on higher education.
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Hide AdEdinburgh University fears its education school budget may be cut by up to 23 per cent, resulting in the loss of 40 full-time jobs. Other teacher-training universities including Strathclyde, Dundee and Stirling are also expected to be hit.
The report stated reducing teacher-training places will cause "major financial problems" for universities and could ultimately harm school education by raising class sizes and reducing individual attention for pupils.