The move was approved at a full council meeting and will see an increase in the general rate by 2.95 per cent, as well as an additional two per cent for adult social care.
It means the rate for an average band D property will rise from £1,231.47 to £1,292.40.
The authority had proposed a 3.95 per cent hike back in December 2018, but tabled a further one per cent increase amid funding concerns.
County council leader, Martin Hill, said the authority faces uncertainty until the government completes a review into future funding.
“We will know this time next year what the future looks like when these consultations finish,” he said.
“We’re hopeful that it could be a better picture, but there is a risk that it could be worse.
“The advice I’ve given to councillors is ‘let’s just wait and see how it all pans out’ and then hopefully we will be in a better position to increase spending on some things or a lower council tax.”
An opposition amendment tabled by Labour councillors called on the council to use some of its reserves for vital services and projects.
Labour leader, Councillor Rob Parker, said the authority had more than £200 million in reserves, £3.05 million of which could be spent on such things as Citizens’ Advice Bureau and childrens’ services.
“People will suffer because they will not get anything this year,” he said.
“Investing for today saves more for tomorrow and enhances people’s lifestyles.”
But, county councillors voted down the opposition amendment.
Meanwhile, the authority is expected to see further cuts in grants from central government.
Money from the council’s revenue support grant, which is the main source of funding from government, is expected to fall to £20.139 million.
It means the authority will have seen a £50.212 million cut in its grant over the past four years.
As a result, the county council has forecast a shortfall in its budget of £3.087 million.
But the authority has proposed to dip into its reserves in order to balance the books.
Council officers said the move would “smooth the effect” of government cuts.