It was constructed by the Duke of Tuscany, Cosimo dei Medici I for the Knighthood of St. Stephen, which was formed on 9 January 1561 to fight against the pirates. The construction was directed by Giorgio Vasari (known more as a biographer than as an artist) between 1562 and 1564.
On the right side (in the photo) of the building, you can see an imbedded large arch; this came from the preceding building called Palazzo degli Anziani.
The decoration of the façade is also directed by Vasari. It is composed in three layers; the lower part is decorated with 12 constellation of the year, the middle with allegorical figures like Art and Virtue, and the topmost with the bust of the Medici Dukes, and at the centre, the famous emblem of the Medici family.
Since Napoleon founded the Normal School in 1810 and gave the use of the building to the school, it is still occupied by the Scuola Normale.