Derbyshire County Council's cabinet provisionally approved the 2017/18 hike during a meeting this afternoon.
The increase, which will generate an extra Â£11million, includes a two per cent rise to help to meet the rising costs of adult social care.
It means a hike of Â£36.16 a year – or 70p a week – for a Band B property and Â£46.49 a year – or 89p a week – for a Band D property.
In addition, councillors agreed to make a further Â£34m of budget cuts over the next year.
A total of more than Â£200m of cuts has already been made. By 2021/22 up to Â£80m must be cut from the council’s overall budget.
Anne Western, leader of the Labour-led authority, said: "We don't want to raise council tax and we know that this places an additional burden on households.
"We're doing everything we can to maintain our services, especially where they are protecting and supporting older and vulnerable people and children who need our care.
"We're always exploring new ways of generating income and saving money, scrutinising every penny that is spent.
"Cutting services is the last thing anyone at this council wants to do.
"However, we are going into our eighth year of Government austerity and we have a legal duty to balance the books."
Following the budget announcement, Derbyshire County Council's Conservative Group accused the council of 'shocking brutality'.
Conservative leader Barry Lewis said: "Derbyshire Labour have gone beyond a joke – they are harming Derbyshire residents' lives with their incessant ideological attacks on the Government.
"It's clear from today's budget proposals and our analysis that they are setting out to grab anti-Government headlines at the expense of Derbyshire residents."
Simon Spencer, deputy Conservative leader, added: "Our analysis shows that the worst of the cuts are behind us and that now it is about anti-Government rhetoric led by the Corbynites at Matlock County Hall.
"This is just shocking brutality to try to create a story, a fiction."
The council tax rise and budget cuts are subject to approval of the full council.