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.