Chancellor George Osborne has promised to increase funding to Arts Council England and national museums and galleries in his Spending Review.
The Department for Culture Media and Sport's (DCMS) overall budget is to be cut by 5% - far less than some feared.
As part of that, the department's administration costs will be slashed by 20%.
But there were concerns over the future of museums, galleries and theatres that rely on funding from local councils.
Mr Osborne told the House of Commons that the Arts Council and the UK's national museums and galleries will get a cash increase between now and 2020.
Arts Council England's grant is expected to rise by between 1-2% over the next five years.
The settlement means it can continue to fund its 684 theatres, museums, galleries, dance, opera and ballet companies and other cultural organisations at current levels until 2018.
National museums will also remain free to enter and Mr Osborne promised to "look at" a new tax credit for museum exhibitions.
"Deep cuts" to the department would be a "false economy", Mr Osborne said, telling the House of Commons that £1bn a year in grants adds £250bn to the economy.
"One of the best investments we can make as a nation is in our extraordinary arts, museums, heritage, media and sport," he said.
As well as Arts Council England, the DCMS funds national museums and galleries including the Tate, National Gallery and British Museum, plus institutions like the British Library and British Film Institute.
Analysis by Will Gompertz, arts editor
Ed Vaizey, the Minster of State at the DCMS, said the Comprehensive Spending Review settlement for his department was "the best news the [subsidised] arts have had for six years," adding: "The arts have proved their worth to The Treasury. Ask any visiting dignitary or tourist in the street and they want to go to our museums and theatre."
Peter Bazalgette, the chairman of Arts Council England, was equally pleased with the Chancellor's decision to give ACE and the national museums a "flat-cash" settlement. Having looked at the numbers, he said that put ACE "slightly ahead in cash terms", when taking into account the negative impact of inflation and the positive impact of new "parcels" of money.
Bazalgette said the Treasury had listened to and recognised the arguments made to it over the past five years by the arts sector, which were based on the "positive benefits the arts confer on society in terms of education, tourism, regeneration, economic impact, quality of life and Britain's brand abroad".
The Creative Industries Foundation also welcomed the Chancellor's "recognition" of the arts and their value to the economy, but stated a concern for arts organisations outside London, which it said could be impacted by "the deep cuts to local authority budgets".
Many in the arts had been braced for a deeper funding reduction. Fiona Gasper, executive director of the Royal Exchange theatre in Manchester, summed up the mood of many in the arts when she said she was "relieved".
She said: "I don't think anybody expected that the Arts Council would not get a cut. The figures that were being bandied around were 25% to 40%. So we were all braced for something that would have significant impact.
"I'm really quite delighted and an awful lot of work has gone into trying to make the case that it's not worth cutting us because actually we're quite a good deal for the small amount that goes into us."
More museums 'likely to close'
However, many museums, galleries and performing arts organisations will fear the repercussions of cuts to local government budgets.
Museums Association director Sharon Heal welcomed Mr Osborne's decision to protect the Arts Council England budget and preserve free entry to national museums.
But she added: "We remain deeply concerned about the impact of the local authority budget cuts on the UK's civic museums, and on the huge number of people who visit them.
"We believe that civic and local museums up and down the country will face real difficulties because of local authority funding cuts over the 2015-20 period - particularly those in less well-off areas.
"Museum closures, job losses and the introduction of charging are happening already. Today's Spending Review means that this trend is likely to grow."
The Comprehensive Spending Review also included other provisions for arts and culture, some of which had been announced previously:
- £150m for new "world-class storage facilities" for the British Museum, Science Museum and Victoria and Albert Museum.
- £78m to build the new Factory arts venue in Manchester plus £9m per year to run it from 2018-19. The venue will be designed by architect Rem Koolhaas.
- £20m for a Great Exhibition of the North and a new Great Exhibition Legacy Fund "to pave the way for future cultural investment in the Northern Powerhouse", to be run by Sir Gary Verity.
- £5m for a new South Asia Gallery at Manchester Museum.
- £4m for a Birmingham Dance Hub.
- £2.5m for the Museum of Science and Industry in Manchester.
- £1m "to create a lasting legacy" for Hull's UK City of Culture 2017 and prepare for the next UK City of Culture.
- £500,000 to celebrate the 400th anniversary of the Mayflower in Plymouth in 2020.
Tim Plyming, director of digital arts and media at innovation charity Nesta, said he was pleased with the settlement but that arts organisations still needed to look for new sources of funding.
"The risk is to sit on our laurels," he said. "We're encouraging organisations to think outside a very narrow funding environment. A lot are reliant from grants from one or a few sources.
"We want to encourage a more diverse funding model - a greater emphasis on philanthropy and the growing social investment funding environment that there is."