In 1524 Clement VII had ordered Michelangelo to design and construct a building in which to place the Medicean library, purchased by Leo X and kept by the Dominicans on the premises of the Church of San Marco. In 1558 the building destined to house the Medici Laurentian Library, inserted in the monumental complex of the Church of San Lorenzo, was completed. The Library was opened to the public for the first time in 1571.

The Library contains precious works also as regards scientific topics. In 1491 Agnolo Poliziano wrote to Lorenzo the Magnificent, who had requested him to search for important scientific manuscripts, that he had found in the library of Giorgio Valla "some books by Archimedes... that are lacking to us". Of those manuscripts, known as Codex A, Lorenzo had a copy made, which is conserved today in the Laurentian Library and which constitutes the most important example of the Archimedean Corpus, Valla’s original having been lost. During those same years Giovanni Lascaris, again at the request of Lorenzo, found in Greece the precious collection of ancient medical texts, including the writings of Hippocrates, that had belonged to the Byzantine physician Niceta, today included among the Library’s collections. The library also possesses the Greek and Latin codices and manuscripts of the Camaldoli Monastery and the Naturalis Historia by Pliny purchased by Cosimo the Elder at Lubeck, which constitutes the first complete codex of the important naturalist encyclopaedia, later translated by Landino.