The house got its name from its owner Juraj Apponyi. Thanks to his radical reconstruction, the originally older Baroque house was modified in 1761–1762 into its current appearance, however, the interior decorations were preserved.  

In 1867 the city bought the house for the municipality and had the city‘s coat of arms added into the cartouche over the gate. Already the 1904 plan of the house features the rooms on the ground floor labelled as City Museum‘s premises. In 1926 the Museum opened an exhibition on its 1st floor piano nobile, in 1930 a gallery on the 2nd floor and the following year the Bratislava Museum of Viticulture on the ground floor. In the next decades, the 1st floor connected with the Old Town Hall was used for exhibition purposes. The 2nd floor firstly served for offices, later on as a deposit and the Regional library.

The 2004–2008 saw an extensive renovation of the house and after its completion the Museum established exhibitions of the Period Rooms Museum and the Museum of Viticulture, the study deposit of the ceramics, china and glass in the loft. The house became an individual building without any connection with the Old Town Hall.