Established by the Hungarian Parliament in 1896, the Museum of Fine Arts united previously separate collections of classical art. The building was designed and constructed by Albert Schickedanz and Fülöp Herzog in an eclectic-neoclassical style between 1900 and 1906.

The museum's collections today house more than 100,000 pieces in six curatorial departments: the Collection of Egyptian Antiquities, the Department of Classical Antiquities, the Old Masters’ Gallery, the Collection of Old Sculptures, the Department of Prints and Drawings, and the Department of Art after 1800.

As a legal body, the museum incorporates several other institutions as well: Artpool the Art Research Center (since 2015), the Ferenc Hopp Museum of Asiatic Arts (since 2014), the Hungarian National Gallery (since 2012), and the Vasarely Museum (since 1987).