The museum had its origins in the Seattle Fine Arts Society (organized 1905) and the Washington Arts Association (organized 1906). These two groups merged in 1917 into the Art Institute of Seattle. The Art Institute housed its collection in Henry House, former home on Capitol Hill of the collector and founder of the Henry Art Gallery, Horace C. Henry (1844-1928). Fuller was active in the Art Institute and became president in 1931. The museum in Volunteer Park was designed by Carl F. Gould (1873-1939) head of the University of Washington's School of Architecture and principal architect of the University's "college gothic" buildings.
In December 1991, the museum opened a new building in downtown Seattle at 1st Avenue and University Street. The Volunteer Park museum became the Seattle Asian Art Museum.