Their decision has come in response to a national consultation on the process for identifying potential sites.
In May 2015 the Welsh Government adopted a policy supporting geological disposal for the long term management of higher activity radioactive waste.
A programme, funded by the UK Government, has been set up to seek a single disposal facility from Wales, England and Northern Ireland and will be delivered by Radioactive Waste Management Ltd.
In January the Welsh Government issued a policy statement setting out the broad outline of arrangements for working with potential host communities in Wales, should any wish to seek discussions about potentially hosting a geological disposal facility in Wales.
Councillor Tony Thomas, Cabinet Lead Member for Housing, Regulation and the Environment, said: “At a meeting of the full council, councillors agreed to respond to the consultation, expressing their firm views that they want the county to be nuclear-free and would not support any such facility in the county.
"They raised concerns about the effects on the landscape, the environment and on future generations in the county.
“Whilst we welcome the opportunity to respond to the consultation, we will be setting out our objections in the clearest of terms and forwarding our response to Radioactive Waste Management Ltd.
"We will also be contacting other councils in North Wales to see whether they wish to issue a regional response."