Proposals to introduce a voluntary severance scheme were approved after a meeting of the ruling Court of Dundee University.
Professor Pete Downes, the university principal, said: "To deliver our ambitious transformation vision we need to encourage excellence across all academic areas and to be able to invest in our future strategy at a time of unprecedented pressures on public spending and challenging future financial projections.
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"Through our operational planning process we are looking to identify opportunities to generate additional income to support investment.
"However, at this point in our analysis, we have identified that we need to achieve reductions in academic staffing levels across the university."
Mr Downes said no target on job losses had been set, but it is understood the institution wants to cut between 80 and 120 staff.
The university said it would try to avoid compulsory losses.
The union that represents academics and support staff said the university should look to save money in other ways.
Mary Senior, Scottish official of the UCU union, said: "Staff at the university are deeply shocked and worried at claims of significant job cuts."