“In 1592,” writes Baldinucci in his life of Matteo Nigetti, “Alessandro Strozzi bought a house from Camillo de’ Pazzi, that same Camillo who was father to S. Maria Maddalena, and a small one adjoining with a shop, at Canto del Papa, so-called in olden times from a family who lived there, but afterwards called the Canto de’ Pazzi; near to where the first wall of Florence ended towards the east with the Porta S. Pietro.” They were bought with the intention of building the fine, but unfinished, palace we now see, and Alessandro charged Bernardo Buontalenti not only to make the design but to superintend the work. Nigetti worked under him for seven years, until the façade as far as the sills of the first floor windows on the side towards the Duomo was finished. “The kneeling windows and the door in Borgo degl’Albizzi show how great was the talent of Buontalenti,” says Vasari; “he only built the first floor of the palace, as a difference arose with the owner about a certain staircase proposed by Santi di Tito, who did what little he knew and no more, and the building was then entrusted to other hands.” Scamozzi the Roman architect was at that time in Florence and continued the work for Ruberto Strozzi. When he left, Caccini became the architect and sculptured the fine coat of arms at the corner, shown in the drawing. After his death Nigetti was once more called in to superintend, and Cigoli designed the courtyard. The Guasti family bought the palace in the XVIIth century, and the entrance court, which till then had been open, was roofed over. With so many architects it seems strange that the palace should have remained in such a condition as to have merited the special name of Nonfinito (the Unfinished) in a city where but few of the great buildings are completed. It is possible that some dispute arose between the Strozzi and the Salviati, whose palace was opposite, about the height; in which the latter, connected with the Medici by the marriage of Maria Salviati with Giovanni delle Bande Nere, would have gained the day.

In 1814 the palace was bought by the Grand Ducal government, and Fossombroni, the enlightened minister of Fernando III., inhabited it for some time. It then became the office of the head of the police, and now is the central telegraph office of Florence.