The council also agreed to a range of other measures to deliver the required £11.3 million in savings for 2017/18. However the ruling Labour/Tory administration says there will be no compulsory job losses or service reductions.
Council leader Rhondda Geekie said: “We have had to reduce our council budget by £53 million over the past ten years - with almost £31 million of that during this current five-year term.
“And although a further cash injection was announced earlier this month, equating to an additional £3 million in revenue and capital for the area, the fact remains that our funding gap for 2017/18 is £11.3 million.
“This is the highest funding gap we have ever faced - and requires significant further savings to be found.”
A 3 per cent increase will see council tax on a Band D property in East Dunbartonshire increase from £1,141.85 to £1,176.11 - a rise of £34.26 per year.
This will deliver an additional income of almost £1.8 million to the council for the year.
Householders in band E to H properties will face an additional rise in council tax after the Scottish Government voted to raise the charges for these bandings at the end of last year.
The Liberal Democrat Group put forward a motion to increase council tax by 2.5 per cent.
They also asked the council to set aside £50,000 for swimming lesson for school pupils and £490,000 for road and pavement resurfacing.
However this did not get enough votes from the other councillors.
A motion put forward by the SNP group was more successful and has been incorporated into the administration’s budget.
This includes a commitment to report back to the council about proposals which will affect school management structures, after full engagement with headteachers and teaching unions.
A pilot scheme for a Breakfast Club, with a provisional budget of £100,000.
A dedicated support resource for community councils and a pilot scheme which will allow more schools to access leisure trust facilities to increase their physical exercise - including swimming.
Council house rent will also rise by 2.5 per cent.