It will add 75p a week to a Band D council tax (9%), which is in line with the treasury's own predictions for council tax increases this year.
Council leaders have pledged that all of the additional £5.8m will go direct to frontline services, £5m to schools (not other education services) and £800,000 to social services. None of the cash will be kept back for central administration.
Labour leader Janet Jones explained the council's rationale for setting this cap-busting budget.
'We're happy to do that but it takes our budget nearly £6m above our spending limit.
'If the minister asks us to explain ourselves in the spring I believe we can put forward a convincing and compelling argument to justify our actions.'
Liberal Democrat leader Peter Lee explained that despite going above the spending limit people should not be deluded into believing there would be no cuts to services.
He said: 'We will still be forced to close four libraries and reduce opening hours at other libraries. Our transport budget will face a cut of nearly £2m (6%), the cuts to community education will still go ahead, and whilst social services will get some relief they wills till be suffering reductions of £2m.
Cllr Lee called for a fair deal for Cambridgeshire, adding: 'We are one of only two counties whose cap prevents us from spending above our SSA, and, once again, we have failed in our bid to be awarded the area cost adjustment that rewards neighbouring authorities like Bedfordshire.'