Tasmanian treasurer Peter Gutwein cited RBF's declining membership, lack of scale and rising costs as the reasons behind the proposed merger with Tasplan and Quadrant.
Mr Gutwein said a review of RBF found it would be "increasingly difficult" for the fund to "continue to provide the same high-quality service to members".
As a result, Tasplan and Quadrant, which announced their (separate) merger in November 2014, have entered into a memorandum of understanding with RBF.
The merger of the three funds would create an entity with around 165,000 members and $6.5 billion in funds under management.
The Tasmanian government recommended the merger of all three Tasmanian superannuation funds to avoid the loss of local jobs created by a merger between RBF and a 'mainland' super fund.
"The creation of the new super fund will secure Tasmanian jobs and ensure that Tasmanians continue to benefit from the presence of a competitive and viable superannuation fund in their state," Mr Gutwein said.
"Once it is up and running, the new super fund will become the default fund for Tasmanian public sector employees, and importantly, members will retain their choice of superannuation fund."
A statement by Tasplan and Quadrant welcomed the Tasmanian government's support for a single Tasmanian superannuation fund, noting that the earliest a merged fund would be "up and running" would be the end of 2016.
Wayne Davy, the chief executive of Tasplan/Quadrant, said the merger of all three funds would be "extremely positive" for the future of superannuation in Tasmania.
"The RBF Tasmanian Accumulation Scheme merger is a huge step for Tasplan and for the state," Mr Davy said.
"Until we progress the merger, we won’t know exactly what the merged fund will look like – for example, what fees, insurance and investment options the merged fund will offer.
"However, the law says we can’t merge unless we can show that the merger is in the best interests of our members," Mr Davy said.
