The studios, based at the Roundhouse creative centre and music venue in Camden, north London, works with thousands of 11 to 25-year-olds including those who are disabled, homeless, out of education or training, excluded from school or at risk.
Money from ticket and refreshment sales at the venue goes to support the work of the studios, which will be renamed the Paul Hamlyn Roundhouse Studios as a result of the donation.
Marcus Davey, chief executive and artistic director of the Roundhouse, said the money would help to secure the future of the studios.
"In the foundation, we have a partner that is just as committed to this work as we are," he said. "The foundation has been a much-valued supporter of our 11-to-25s programme ever since the reopening of the Roundhouse – and the launch of its studios – in 2006, and we greatly appreciate its continued support."
A spokesman for the foundation said the money would be invested and the proceeds spent on supporting young people through music, media and performing arts. It could also be used to cover their core costs, he said.
The foundation has had a long-running relationship with the Roundhouse. One of the last projects its founder, the publisher Paul Hamlyn, worked on directly before his death in 2001 was the redevelopment of its grade II listed building.
Jane Hamlyn, chair of the foundation set up by her father, said: "In our 25-year history, the foundation has supported hundreds of organisations working with thousands of young people facing big challenges to make their way in our world.
"Today those challenges are tougher than ever. The foundation backed the Roundhouse’s vision early on, and we’re delighted to mark our 25th anniversary with this special gift."
The Paul Hamlyn Foundation is due to announce similarly large endowments to several other charities this year to mark its 25th anniversary.
Each will be related to the foundation’s mission to improve quality of life and maximise potential through its areas of interest – the arts, education and social justice.
The foundation is one of the UK’s largest and was worth £559.6m at the end of 2011/12. It awards grants of about £20m a year in total.