Palazzo Albizzini is a late 15th-century building in the style of the sober and essential architecture of the Florentine Renaissance and is located in the historic center of Città di Castello; its total area is 1660 square meters and it is divided into three floors.

The palace, which belonged to the Albizzini family (known for having commissioned Raphael, in the Church of San Francesco not far from the building, to paint the Marriage of the Virgin, now housed in Brera) was identified by Burri to concretize his desire to establish a foundation of a private nature with suitable headquarters to permanently house a body of works he had selected.

The building was purchased by the Cassa di Risparmio di Città di Castello (an institution now merged into Banca Intesa) and granted to the Fondazione Burri on a free loan for ninety-nine years beginning in 1978, the year of its establishment.

Restoration work on the Palazzo, promoted by the Bank itself, began immediately and was conducted by Alberto Zanmatti assisted by Tiziano Sarteanesi, both under the guidance of Alberto Burri and Nemo Sarteanesi. The Renaissance structure was respected; the white walls and pietra serena do not contrast at all with the works masterfully arranged by Burri; each of them enjoys ample space to allow maximum enjoyment for the viewer. At the time, state-of-the-art equipment was employed in the building.

The museum was opened to the public on December 12, 1981.

The 150 works on display, included in a chronological span from 1948 to 1985, are Tars, Molds, Humps, Sacks, Woods, Metals, Combustions, Cracks and Cellotex as well as a sculpture and sketches for stage sets and for some pictorial cycles exhibited at the Ex Seccatoi del Tabacco.