The facility in Johnstone, Renfrewshire will also house a library, theatre and marriage suite as well as space for community use.
It will bring a host of Renfrewshire Council services together in the centre of town. These will include customer services, housing, social work and the council's registration service.
The old pool facilities have been transferred to the new Johnstone sports hub which opened in the summer.
Convener of Renfrewshire Council's community and family care policy board, councillor Iain McMillan, said: "Regenerating Johnstone is high on our agenda.
"Residents already benefit from the £6.9m Johnstone sport hub and this demolition work marks the start of another £14.5m being ploughed into the town's infrastructure.
"We will do everything we can to support local people and the traders.
"We will also continue to consult with the families and firms that make up the community of Johnstone to ensure we deliver the facilities that meet their needs.
"This is a positive step for Johnstone with the first signs on the ground of the massive investment in new facilities."
During the work the public car park at Houstoun Court will remain open.
Pedestrian access from William Street to the town hall and library will also be kept open while the swimming pool is demolished.
Temporary changes will be needed to the way traffic is managedand this is likely to include a one-way system in William Street.
Reigart Contracts is carrying out the demolition.
The planning application for the new civic hub is due to be submitted later this month and an open evening will be held on November 13 in the existing town hall.
It is thought the new town hall will open by December, 2013.