It said the move was part of a drive to meet the government's requirements for improved efficiency in the public sector as set out in the Gershon Review.
The decision will help to build the momentum behind open source software in the public sector, according to a senior analyst.
Ovum government practice director Eric Woods said it was significant that the council cited the Gershon Review to justify its decision. "Councils are looking at how they can respond [to the call to cut costs and improve efficiency]. This will not be the last time a council makes this decision. We expect the momentum to build," he said.
Last month an Office of Government Commerce report said open source software, including Staroffice, Sun's licence-free alternative to Microsoft Office, was suitable for deployment and could offer savings to the public sector.
Bristol plans to introduce Staroffice to more than 5,000 users, replacing the council's existing mixture of Corel's Word Perfect, Lotus 1-2-3 and Microsoft Office software.
Most departments will transfer to the new software, although about 1,800 desktops in the city's education service will remain on Microsoft Office.
Bristol council piloted Staroffice on 600 desktops in the housing department.
Stewart Long, head of IT at the council, said the product performed well in terms of functionality and compatibility. The main lessons came from training and informing staff.
"The roll-out will be over 12 months with lots of communication and training. The housing project was a bit rushed, but Staroffice still seemed the right product. These lessons would apply to any desktop software," said Long.