Siptu represents the 615 workers employed by G4S and they voted on Thursday by 79 per cent to 21 per cent to accept the proposals.
Commenting on the outcome of the ballot, Siptu organiser Brendan Carr said: "The company's restructuring proposals envisage approximately 30 voluntary job losses and changes to workers' terms and conditions of employment."
Earlier this week, The Irish Times revealed that G4S had warned customers recently that, unless they agreed to revised terms and higher prices by August 5th, its UK-based parent company would withdraw its financial support for the loss-making business.
It is understood that price increases of more than 10 per cent are being sought from customers.
Failure to secure continued financial support from its parent would have left the company insolvent and dependent on a possible examinership process for its survival.
In a presentation to clients to outline its financial difficulties, the company forecast a loss before interest, tax and amortisation of €10.07 million. Its turnover has declined from €48.2 million in 2009 to an expected €38.5 million this year.
G4S also indicated that it would be seeking up to 100 redundancies among its workforce and changes to their terms and conditions. The company yesterday declined to comment on the outcome of the ballot.
It is not clear if G4S has persuaded its customers to accept higher prices for its services.
The company has a 63 per cent share of the cash-in-transit market in Ireland and transports about €50 million around the State each day.
Its customers include most of the main banks, An Post, Dunnes Stores and Boots.
G4S operates from nine sites in Ireland and replenishes 370 ATM machines each week and visits 11,520 other outlets on a daily basis. Its parent company is listed on the London and Copenhagen stock markets.