The building that houses the Musem (that was opened to the public in 1869) is the old convent of Dominican order, restored and enlarged to its present size for Cosimo the Elder de' Medici by the architect Michelozzo (1396-1472). Consacrated in 1443, this building was the scene of fervent religious activity and played host to personalities like S. Antonino Pierozzi, Bishop of Florence, Beato Angelico (c.14001450) and later Girolamo Savonarola.

The Museum offers visitors an example of a perfectly preserved 15th century convent, based on the rational and harmonious plan inspired by Bruschelleschi's innovations. On the other hand, the complex also contains the works of Fra' Angelico, a Dominican monk who closely collaborated with Michelozzo and his pupils to the fresco of the large alms-house, the refectory, the cloister and the monks' cells on the first floor. One of the most famous frescoes is the (Crucifixion painted in the Chapter House, permeated by the contemplative melancholy found in the refined spirituality of the Dominicans.
Among the frescoes of the cells, which are austere yet full of meditative inspiration for the brethren, we find the Annunciation, the Three Maries at the Tomb , and the Noli me tangere.

The panel paintings in the Refectory comprise the earlier works of Angelico,in addition to a superb reredos showing the Last Judgement and the Deposition set against the background of the Tuscan hills. In addition to the works of the Dominican Fray, the museum displays a beautiful Last Supper frescoed by Ghirlandaio at the end of the 15th century and a fine series of paintings by Fra' Bartolomeo, who spent some time in the convent at the beginning of the 15th century and to whom an entire room is dedicated. The Large Refectory is instead dedicated to the painters of his school. The Library (one of the most harmonicus examples of Renaissance architecture) displays a fine collection of illuminated manuscripts produced in the convent that reflect the same spirit of meditative creativity. In addition to the cell that once belonged to Savonarola, it is also possible to visit the cells where Cosimo the Elder retired to meditate.

The Visitor's Area and the underground room display a tidy and well preserved collection of precious objects and relics that were saved from the 19th century destruction of the convent, in addition to a rare collection of bells.