Committee chairman Larry Baldock was pleased with the decision, saying it was the best solution.
"A new building provides us the opportunity to deliver a fit for purpose central library service and strongly supports a more vibrant, safe and successful city centre.
"We have received a clear message from our community to 'do it once and do it right', and the decision to plan for a new building is in line with that," Cr Baldock said.
The business case for a new central library will form part of a broader business case for cultural facilities including plans for a museum.
Formal consultation on the redevelopment of the central library and the future use or demolition of the current library building will take place as part of the Long Term Plan process in early 2018.