Nicola Sturgeon revealed higher charges are to be brought in for those living in properties from Band E through to Band H - a move which will bring in extra cash of £100 million a year for schools.
In addition the council tax freeze, which has been in place since 2007, is to be ended from April next year.
From that point councils will be able to increase the charge by a maximum of 3% a year, potentially allowing authorities to raise up to £70 million to help fund local services across Scotland.
From April next year the amount that residents in homes rated from Bands E to H pay in comparison to an average Band D property will be increased.
The council tax bill for a Band H property is currently twice that charged on a Band D home, and this is to be increased so it is 2.45 times the Band D payment.
The Scottish Government estimates this change could cost these families about £10 a week - or more than £500 a year.
But ministers stress three quarters of families who live in homes which are in Band D or below would not be affected by the change to the band system.
In addition some 54,000 low income households who are living in Band E to H homes will be entitled to an exemption through the council tax reduction scheme.
Ms Sturgeon said: "These reforms to council tax bands will mean no change for three out of every four Scottish households, with those in lower banded properties paying no more than they do now.
"Households will also still, on average, pay less than those on equivalent bands in England and less than they would be paying had the council tax freeze not been in place."
She added: "To support those on low incomes and provide additional support to families we will also increase the child allowance within the council tax reduction scheme by 25% - this will benefit 77,000 households by an average of £173 per year - around £15 per month. This boost for low income families will help nearly 140,000 children across Scotland.
"We will also extend the council tax reduction scheme to exempt 54,000 households on low net incomes, but who live in higher property bands, from the change to the system."
The change was announced after a report by the cross-party Commission on Local Tax Reform last year called for an end to the council tax and urged politicians to implement a fairer, more progressive and transparent tax to fund local services.
Ms Sturgeon said: "The Commission on Local Tax Reform made clear that the present system could be made fairer. We are choosing to do this in a reasonable and balanced way that will also generate £100 million of additional revenue to invest in schools."