Shona Robison, the Scottish Finance Secretary announced £144m to help pay the additional cost imposed by the UK Government.
Robison revealed the funding as the Scottish Budget passed its first hurdle after a vote in Holyrood and said it should prevent big council tax rises to cover the cost
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She said: “By providing councils with the equivalent of a 5% national increase in council tax, the certainty I offer today should reduce the pressure on council tax decisions locally and help councils avoid inflation busting increases.”
She added, however, it was “essential the UK Treasury fully fund the costs for Scotland’s public sector”.
Glasgow City Council will meet later this month to set its budget and the level of council tax rise for households across the city.
MSPs voted in favour of the budget at stage one after LibDem and Green MSPs agreed a deal with the SNP to give their support.
The bill will progress to Stage 3 before it becomes law and spending is allocated to the various departments including health boards and councils.
Robison accused the UK Government and Chancellor Rachel Reeves of punishing Scotland’s public sector with the rise in employer’s national insurance contributions stating it could cost £700m.
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The £144m from the Scottish Government will not cover the full cost to the country’s 32 councils but is estimated to be around 60%.
The Conservatives voted against and Labour MSPs abstained.
Michael Marra, Labour finance spokesperson, said: “We desperately want to see Labour’s record investment improve delivery on the front line.
“But we will not vote for this Budget because we very much doubt that it will.
“Years and years of evidence tells us that that is the case, the complete lack of delivery.”
Craig Hoy, Conservative, finance and local government, spokesperson, said: “This is a day of betrayal for Scottish workers and businesses.
“This budget offers no material benefits whatsoever to hard-working Scots. It will damage business by hiking the tax burden by up to £1.7billion.
“It fails to tackle waste, drive reform or deliver growth.”
The Greens and Lib Dems said they won concessions from the Scottish Government in key areas.
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Ross Greer, Greens finance spokesperson, said: “I can list a long list of achievements for people and planet as a result of the Greens engagement in this Budget, compared to a Labour Party that got everything it asked for out of this Budget, because it simply asked for nothing.”
Alex Cole-Hamilton, Scottish Lib Dem leader said his party will “always act responsibly and try to find common ground where it exists”.
But he added support for the Budget does not equal support for the Government, which he says has failed Scotland.
