Members of the GMB union at Glasgow City Council backed walkouts by 72 per cent and other forms of industrial action by more than four to one.
The union is in dispute over changes to working time arrangements, including plans to convert public holidays into annual leave, which it says could cost workers up to £500 a year.
It said it will notify the council of strike dates, warning that the action will hit key services including cleansing, refuse, land and environment, bereavement and social care.
Benny Rankin, a GMB Scotland officer, said: “Our members are taking a stand to resist the threat of poverty pay and to fight for decent public services under public ownership for the next generation.
“It is the lowest paid across the council who are bearing the brunt of the Scottish government’s austerity agenda, with £130 million worth of cuts to the city’s budget expected over the next two years.
“Time and again we have told the council that our members cannot sustain these cuts and that the holiday imposition would force a dispute.
“Perhaps now they will take their employees’ concerns seriously and finally recognise the severity of this situation.”
Glasgow City Council needs to make savings of at least £130m over the next two years as a result of the cuts imposed by the Scottish and Westminster governments.
Councillor Martin Rhodes, executive member for personnel, said: “The city is dealing with the worst cuts ever imposed by the Scottish Government and we recognise the impact they are having.
“We’ve been in continuous discussions with the union to explore ways we can work together to mitigate against these cuts. We’re willing to continue that dialogue and we would hope there would be no need to take industrial action.
“We have given staff a commitment to having no compulsory redundancies and our employees will continue to have some of the best terms and conditions anywhere.
“The real issue here is the chronic under-funding of the city by the Scottish Government. We are prepared to work with everyone for a fairer deal for Glasgow.”