Chancellor Gordon Brown has pledged £12m in his budget speech to improve training for people working in the arts in England.
The cash will "help find the next Serota", arts chiefs said
Culture Secretary Tessa Jowell welcomed the money, saying it was important for the future of the arts in England.
The funding will be spent training people up to be able to run large galleries and museums in the future.
Arts Council England, which distributes government money, said it was "welcome news and we're absolutely delighted".
A spokesman added the money would help the next generation of "Tony Halls and Nicholas Serotas".
Mr Hall is the chief executive of the Royal Opera House while Sir Nicholas was appointed director of the Tate galleries in 1988.
The package only applies to England - other parts of the UK have their own arrangements for funding the arts.
Ms Jowell said: "Our artists and arts institutions have an international reputation for excellence.
"But we need to make sure the management and leadership of these companies matches up to the art.
"That's why we're investing in skills to help correct this. We've got the what right, this new money will help us get the how."
A spokesman for the Department for Culture, Media and Sport (DCMS) said it was important to have a clearer career structure for the future arts leaders.
"The arts is a big and growing commercial sector in the UK in terms of turnover and the number of people employed," he said.
He added the DCMS would be working initially with Arts Council England and the Learning and Skills Council to come up with training models.
An Arts Council England spokesman said: "It's really about funding the next generation of leaders and bringing up that kind of talent.
"It's not just getting the cash, it is also the very clear recognition of arts and culture in the wider economy."