Mr Corbyn said a Labour UK government under his leadership would restore £42.8 million in cuts made over the past six years.
His campaign said that included lost grant-in-aid and expenditure of £24 million in real terms for Arts Council England, £9.6 million for Creative Scotland and £9.2 million for the Arts Council of Wales.
The cost would be met from £670 million raised by reversing the cuts to capital gains tax brought in by former chancellor George Osborne in the last Budget.
Mr Corbyn said: “Devolution has given the nations and the regions the chance to develop their own cultural identities and enrich us all, and I’m very keen that that should be the case.
“Labour will protect this and ensure that we place funding for the arts and culture on the secure financial foundations they require in every part of the country.”
The Labour leader said Scotland, where arts and education policy is devolved, would receive at least an additional £13 million in consequentials through the Barnett formula as a result.
Speaking at an Edinburgh Festival Fringe venue, Mr Corbyn said he would aim to put the arts “at the heart of policy-making”.
He said: “There’s something very special about the Edinburgh Festival because it obviously is a fantastic city, but the world comes to Edinburgh during August for the festival and it is truly international.
“And of course the origins of it go back to the post-war period when the inclusion of arts in national policy was included during the Second World War.
“That led to the Festival of Britain, it also led to the origins of quite a lot of arts festivals all around the country, and Edinburgh is of course the biggest and best example of that.
“What I’m announcing is a series of policies that will give people the opportunities they need to let culture and free activity thrive and enrich society.”
Mr Corbyn said a Labour government with him at the helm would increase the proportion of GDP spent on the arts and culture to match the European average and bring in a cross-departmental cabinet committee tasked with increasing participation.