Founded in 1927 under the name of Institute and Museum of the History of Science by initiative of the University of Florence, it had a decisive role in the realisation of the First National Exposition of the History of Science (Florence, 1929). The first exhibition halls were opened to the public in 1930 in the venue of Palazzo Castellani adjoining the Uffizi Gallery, which it still occupies today. After undergoing major renovations since 2007, the Institute reopened in 2010 under the new name of Museo Galileo.

The scientific instruments collections of the museum are among the most important in the world. These collections are an eloquent testimony of the promotion of scientific research conducted first by the exponents of the Medici dynasty, and then by the Lorraine Grand Dukes. Starting from Cosimo I, the Medici Grand Dukes started collecting instruments of extraordinary beauty and innovative conception. The Medici scientific collection was initially conserved in the Sala delle Carte in Palazzo Vecchio. Later, it was placed in the Stanzino delle Matematiche and in the adjoining Sala delle Matematiche in the Uffizi Gallery. Continually increasing in size, these collections remained in the Gallery, alongside masterpieces of the figurative arts and the most unique natural wonders, until the mid 18th century when the scientific collections were separated from the art collections.

Transferred to the Museum of Physics and Natural History, founded by Grand Duke Peter Leopold in 1775, the Medici scientific collections were enriched by substantial acquisitions of new instruments and experimental apparatuses. Under its first director, Felice Fontana, the Museum of Physics became an important structure for studies and diffusion of scientific culture. On the occasion of the Third Congress of Italian Scientists in 1841, the Galileo Tribune was built at the Museum of Physics and Natural History, to accommodate the most important instruments of the Medici collection, alongside those invented and utilised by Galileo and the Accademia del Cimento.

In 1860, as a consequence of the Unification of Italy, the Museum of Physics and Natural History was suppressed. Most of the collections were assigned to the Facoltà dell'Istituto di Studi Superiori [Faculties of the Institute of Advanced Studies]. Only the antique instruments and the zoology and anatomy collections remained in their original location. In 1925, the University of Florence was founded, becoming owner of the old scientific collections. In 1927, in order to guarantee their preservation and valorisation, the Institute and Museum of the History of Science was founded, and received the Medici-Lorraine collections of scientific instruments at its venue in Palazzo Castellani. Thanks to the commitment of its first directors, Andrea Corsini and Maria Luisa Righini Bonelli, the Museum of the History of Science of Florence progressively transformed into a centre of conservation, dissemination and research of recognised international importance.

In the course of the past years, the museum layouts have been entirely reconceived; the library has become the Italian centre of reference for studies of the history of science and technology, and of scientific museology. The Institute has organised international conferences and seminars, training courses, and exhibitions destined to prestigious itinerancies. It has also published a large number of volumes of studies and dissemination. Didactic activity has also greatly developed at the same time, accompanied by the realisation of innovative multimedia products distributed both on the Internet and off line.

The current exhibit, whose premises and contents have been radically renovated, develops over two floors of Palazzo Castellani. The exhibition itinerary is articulated along chronological and thematic criteria. The first floor is dedicated to the instruments of the Medici collections, exhibited in nine rooms where visitors can observe, among other things, refined mathematical instruments, Galileo's original instruments (including the only two telescopes of those personally built by the Pisan scientist that have come down to us), the glass instruments of the Accademia del Cimento, and the extraordinary collection of terrestrial and celestial globes, dominated by the monumental armillary sphere by Antonio Santucci. The nine rooms on the upper floor present the scientific testimonies of the Lorraine age. They illustrate the outstanding Tuscan and Italian contribution to the development of electricity, electromagnetism and chemistry, the complex works of both portable and tower clocks, the extraordinary series of obstetrical waxes, the chemistry cabinet of Grand Duke Peter Leopold and, finally, the beautiful and didactically effective machines to demonstrate the fundamental principles of physics, built by the workshop of the Museum of Physics and Natural History.

The restoration of the interior of the Palazzo Castellani (which dates from the twelfth century) has emphasized its monumental dimension and architectural distinction. The elegant, state-of-the-art display cases highlight the esthetic quality of the objects on view, while ensuring their perfect conservation. Portable interactive video-guides—used for the first time in a museum—make the most complex instruments fully understandable even to non-specialist visitors. The devices offer access to hypertext pages, 3D animations, and biographies. Visitors can use the video-guides to select an itinerary through the museum tailored to their specific interests.