Although in the 1830s a small natural history museum existed at the rooms of the Literary and Scientific Society at the Pantiles, the present Museum traces its foundation back to the summer of 1885 when Dr George Abbott began to arrange displays in the Society's entrance lobby. His enthusiasm led to the formation of the Natural History and Philosophical Society and the beginning of their natural history and antiquarian museum.
In 1897 the Borough Council adopted the 1891 Museums and Gymnasiums Act, and later the authority assumed responsibility for the Society's collections. Although building of the town's new Civic Centre began in the 1930s, the Second World War delayed plans to relocate to the purpose-built Library and Museum building. In 1954 the museum moved into its new home which it has occupied ever since.