The total cost of the project is about £470,000, with support already secured from Arts Council England.
Nathaniel Hepburn MBE, director and chief executive at Charleston, said: “The studio at Charleston is a place of global importance – a space where art, life and community came together in radical new ways.
“By supporting Studio 100, donors will help us secure this remarkable building for the next century, making sure its history continues to inspire artists and visitors alike.”
The charity said it needed to conserve to the studio’s roof, windows and doors, and stabilise fragile painted walls and floors.
It will also install a monitoring system to reduce humidity and control the temperature, it said.
Work is scheduled to take place from November 2026 to April 2027, while art pieces in the studio by Bell and Grant are exhibited at Tate Britain.