The council plans to move 5,000 users from a mixture of Corel Word Perfect, Lotus 1-2-3 and Microsoft Office software to Sun Microsystems' integrated Star Office 7 suite.
Using open source desktop applications could save the council £1.4m over the next five years, the council said.
The move is being proposed following successful completion of a pilot scheme run on 600 desktops in the council's Neighbourhood and Housing Services department.
Most council departments would transfer to the new software, although some 1,800 desktops in the city's education service - including schools - would remain on Microsoft Office for the time being.
Stewart Long, the city council's head of IT, said, "We have spent three years evaluating our options and investigating the technical, financial and cultural issues related to migrating our staff to new office software.
"The technical quality of Star Office is good, the business case is accurate and the cultural issues can be managed so that the migration is handled effectively."
Some staff would retain access to Office applications.