"Following more than 40 years in London, the new arrangements signal a bold, imaginative and sustainable future for the EUYO," chief executive Marshall Marcus said in a statement.
"It makes absolutely no sense for the office not to be in the EU," he told the Guardian.
"You can't ask for EU funding and then not be in the EU. The heart of your operation cannot stay in London."
Following an offer from the Italian culture ministry, the respected orchestra, which draws from European Union member states, will be based in Ferrara and Rome from next year.
Orchestra co-chairs John Tusa and Ian Stoutzker called it a "good day" for European musical cooperation.
"We are grateful to all parties for their vote of confidence in the European Union Youth Orchestra," they said in a statement.
The orchestra was established in 1976 and has about 120 players every year, aged between 17 and 24.
Britain, which provided 13 members this year, will unlikely be able to take part in the project after Brexit actually occurs, although the orchestra said it would wait until the outcome of negotiations between the EU and the UK before making a final decision.
Marcus warned that orchestras would find it more difficult to operate in Britain after Brexit.
"Going out of the UK into the EU is going to become more complicated and more expensive," said Marcus.
"The classical music industry operates with very slim margins. These things can be a bit of a killer."
The orchestra has worked with classical music giants including Daniel Barenboim and Leonard Bernstein and has performed in major concert halls including London's Royal Albert Hall and New York's Carnegie Hall.
Some of its 3,000 alumni are now conductors, soloists, teachers, and instrumentalists with major orchestras such as the London Symphony Orchestra, the Berliner Philharmoniker, the Boston Symphony Orchestra, and the Royal Concertgebouw Orchestra.