The budget cuts include reduced spending on roads and building maintenance in 2016/17.
Council leader David Ross said some of the cutbacks would "undoubtedly put strain on services and staff".
The Scottish government has confirmed a £10.3bn funding deal for councils as council tax is frozen for a ninth consecutive year.
Mr Ross said a total of £1.1m would be saved from the roads maintenance budget in Fife.
"No-one wants to reduce funding for the upkeep of our roads," he said.
"But it is an area where we can choose to do less, and so temporarily save money.
"However, in the year ahead we plan to undertake a full review of our roads service, in consultation with the public, councillors and professionals."
The cut is part of more than £13m worth of temporary savings identified by the local authority.
"These are one-off cutbacks which will undoubtedly put strain on services and staff," Mr Ross said.
"These savings will give us some breathing space as we consider ways to transform services and spending on a permanent basis to meet the ongoing budget challenge."
Other savings agreed by Fife Council include:
Mr Ross added that the government had allocated £16.8m extra funding for health and social care. The council agreed to cut back its funding for the service by 3.6%, or £5m, in line with the cut to the council's grant funding.
He said the administration in Fife had planned to propose a council tax increase of 7.5%, a move which would have given them £7m to invest in public services.
"In public feedback, two out of three people said they supported this idea," he said.
"However, the government attached new conditions to our funding package and would have withheld £25m from Fife services if we'd increased council tax, ruling out this option."
A total of £10.9m of the £30.9m savings will be reinvested in services in the region, he added.
Deputy First Minister John Swinney welcomed the agreement of Scotland's local authorities to the financial settlement.
"It is a package that is firmly focused on our joint priorities to deliver sustainable economic growth, protect frontline services and support the most vulnerable in our society," he said.
Councillors in Fife have agreed to a wide-ranging package of savings amounting to £30.9m.