From the early 1930s, David had toyed with the idea of preserving the collection after his death as a privately owned museum open to the public in the building at Kronprinsessegade no. 30. The C. L. David Foundation and Collection did not become a reality until 1945, however, when the Second World War had ended, after David had survived a serious illness earlier that year. From 1948, the collection was open to the public for only a few hours a week on the third and fourth stories, since David then lived on the second and his law office was located on the first. After David’s death in 1960, opening hours were lengthened as the rest of Kronprinsessegade no. 30 was incorporated into the museum.

In addition to providing the financial basis for the museum’s operations, David had also made sure that there were funds for expanding its holdings. The collection of European furniture and decorative art from the 18th century was augmented throughout the 1960s and 1970s, but it soon became clear that the museum’s most important raison d’être in a Scandinavian context was its collection of Islamic art. Since the 1980s, this is virtually the only part of the collection that has been strengthened through purchases. In order to house the growing number of works of art, the neighboring building, Kronprinsessegade no. 32, was bought in 1986. The first expansion of the museum premises in this building – a long room with showcases for Islamic miniatures – was opened four years later. The miniature gallery was designed by the architect Wilhelm Wohlert (1920-2007), while Wohlert Architects were responsible for later remodeling in 1999 and 2005-2009. In this most recent phase, the space allotted to the Islamic collection was doubled and the exhibition completely reinstalled. A new story was also outfitted for the Collection of Danish Early Modern Art.