The opulent neo-Baroque ashlar building with rich sculpting and a remarkable staircase rotunda was designed by the Aachen architect Georg Frentzen, completed in 1905 and inaugurated on November 8, 1905. The building formed the ensemble of buildings around Hoeschplatz together with the Düren Municipal Theater (architect: Carl Moritz), which was donated by Leopold Hoesch's cousin Eberhard Hoesch (1827-1907) and built between 1905 and 1907, and the Düren St. Mary's Church. Since 1905, the entrance area has been adorned by the two monumental bronze sculptures Studium (male figure to the right of the main entrance) and Phantasie (female figure to the left of the main entrance) by Aachen professor and sculptor Karl Krauß.
During the air raid on Düren on November 16, 1944, the theater and St. Mary's Church were almost completely destroyed; the former was also not rebuilt. The Leopold-Hoesch-Museum was one of the few buildings in the center of Düren to survive the war, albeit badly damaged. Thus, the roofs, domes (only the glass, not the construction), parts of the east wing and parts of the upper middle hall (but not the staircase and not the west wing) were destroyed. The reconstruction, completed in 1952, was carried out in a simplified form, abandoning the domes. The listed building was renovated from 2007 to 2009 and, on the initiative of museum director Dorothea Eimert, received an extension by architect Peter Kulka, which was opened in June 2010. The extension increased the museum's exhibition space to nearly 3,000 square meters and was made possible by the financial support of the Günther Peill Foundation.
The museum was closed for renovations from 2007 to 2010, and the renovated and newly added spaces were inaugurated in June 2010. The new extension by architect Peter Kulka, called the "Günther Peill Forum," contrasts sharply with the neo-baroque old building due to its simplicity and clean lines. But both parts of the building are connected by a glass axis and bridges, thus reflecting the exhibition concept of the museum's new director Renate Goldmann, who was appointed in January 2010. The connection between old and new, between historical and modern architecture, and between works from the existing collection and contemporary art allow new perspectives to emerge.
At the end of June 2011, the 80-ton stone sculpture Ursprung by artist Ulrich Rückriem was erected in front of the museum. It is made of Anröchter dolomite.