The city unit in Pitt Street, which has 66 civilian staff, will close next year.
Its work will be transferred to centres in Motherwell and Govan as part of a sweeping rationalisation designed to save £20million by 2017-18.
Union bosses said they had deep concerns over the moves, which will also see control rooms axed in Stirling, Dumfries, Glenrothes and Aberdeen over the next two years.
Gerry Crawley, of Unison, said "'These closures are not about making our communities safe.
"They are budget driven cuts. Scottish Government is cutting £139m from police budgets between now and 2017 and £1 billion over 12 years."
Unions fear the changes will make calls to 999 and the new non-essential 101 service "less responsive".
There are currently 10 control rooms and nine "contact" centres for non- urgent calls spread across 11 sites in Scotland.
Some 300 control room workers have already applied for voluntary redundancy but their applications were put on hold pending the "rationalistion", which had been widely flagged up by senior chiefs over the last year.
Mr Crawley also said police chiefs were looking to change the ratio of officers to civilian staff in the control rooms.
"They are talking about it being close to 50-50," he said.
"We find that unacceptable given that the costs of employing a police officer is much greater than a civilian."
Unison has long argued a decision to maintain police officer numbers means civilian staff are bearing the brunt of cuts being brought under the single force.
Chief Superintendent Val Thomson, the officer in charge of the service, said: "The current structure across the 11 sites is based on the arrangements that were in place under the previous eight force structure in Scotland.
"Moving to fewer, larger centres will enhance our capability to respond to day to day incidents, as well as complex and large scale emergencies."
The force's watchdog, the Scottish Police Authority, will consider the proposals next week. Its chairman, Vic Emery, promised "rigorous scrutiny".
He said: "We recognise this is a complex and sensitive proposal, which has long-term implications for the organisation of policing and the service's engagement with communities."