Chancellor George Osborne has announced a 7% spending cut to the Department for Culture, Media and Sport (DCMS) as part of the Spending Review.
Arts Council England and national museums will share less of the burden with a reduction of 5% during 2015/16.
The cuts, which are less than many arts organisations had feared, were outlined by the chancellor as part of his plan to help reduce the deficit.
Labour has said it will stick to the plans if it wins the next election.
Making the announcement in the House of Commons, Mr Osborne said national museums would have greater freedoms to use their budgets as they saw fit.
This would include setting their own pay structures and opting out of government procurement procedures.
Sir Nicholas Serota, director of the Tate galleries, welcomed the level of cuts.
"It is a recognition by the chancellor, Culture Secretary Maria Miller and Arts Minister Ed Vaizey, and by government, of the important contribution made by culture and creative industries to the life of communities across the country and to the international standing of Britain," he commented.
Sir Peter Bazalgette, chair of Arts Council England, agreed saying the DCMS and the culture secretary had "done a good job in making the case for continued government investment in the arts and culture".
He added the 5% cut was a "best case scenario in what are difficult and testing economic times", though the level of cuts facing local authorities were "cause for concern".
The DCMS was one of several departments to have reached a deal with Mr Osborne in advance of today's official announcement.
The BBC's arts editor Will Gompertz said he had heard negotiations with the Treasury had been "tough", with Liberal Democrat Danny Alexander "being the hardest to persuade that it made economic and political sense to treat the arts leniently".
Sir Nicholas Hytner, director of the National Theatre said Mrs Miller and her team had "done well" to limit the cut in the national arts budget to 5%, given the context of overall reductions in public spending.
But Richard Mantle, general director of Opera North, which currently receives £9.8m from ACE, said while the figure was lower than initially anticipated, it "doesn't get us out of the woods".
"It's a 5% cut on top of a period of quite severe cuts that have gone to arts organisations since 2011, so it's the cumulative effect which is the challenging thing," he said.
Regional arts organisations, which receive a proportion of their funding from councils, were less content with the outcome of the Spending Review.
Reduced regional services
Keith Merrin, director of Woodhorn Museum in Northumberland said many venues would struggle as a result of a 10% cut to local authority budgets.
"The belief that philanthropy will pick up the slack is simply unrealistic in most parts of the country," he added.
A similar point was echoed by Museums Association director Mark Taylor.
"Predictably, local government is low down the food chain and we know that local government museums or independent museums supported by them are way down the local government food chain," he said.
"The result can only be less museums, open less and providing less services," he said.
Sally O'Neill, interim Chief Executive of the Royal Opera House, said the ROH would work to support colleagues across the sector, including those in the smaller and regional companies "who play such a vital role in the creative industries".
The Treasury wrote to government departments earlier in the year, warning most ministers they would have to cut up to 10% of their budgets for the year 2015/16 under plans to slash spending by £11.5bn.
Culture Secretary Maria Miller was initially reported by the Financial Times to have refused to agree to any cuts to her department.
Arts Council England (ACE), which funds 696 arts organisations across England, had said a 10% cut to its budget could force it to remove regular funding from hundreds of organisations.
In Mr Osborne's first Spending Review in 2010, ACE had its budget cut by 30%, followed by smaller cuts in subsequent years. The Arts Council has already halved its own administrative costs.
Mr Osborne called for the fresh round of belt-tightening in Whitehall - on top of the billions being cut from departmental budgets between 2011 and 2015 - as he tries to get to grip with the deficit in the public finances.
The next general election is scheduled for May 2015 and the Conservative-Liberal Democrat coalition has to set out its budgetary plans for the final few weeks of its time in office, irrespective of the outcome of the poll.
Labour has said it would match the coalition's current spending totals for the full one-year period if it wins the election.