The museum is located in the former monastery of San Bernardo which was built in the 14th century with 17th and 18th century interventions. The monastery was built on the remains of a Roman amphitheatre which dates to the middle of the 2nd century CE and which are visible on the ground floor.
The museum dates back to the 19th century when the collection of the Laymen's Brotherhood was opened to the public. In the 1930s the archeological collection was separated from the medieval and modern collections and given its own space in the monastery of San Bernard. It baecame a state museum in 1973. It is named for Gaio Cilnio, an Aretine who lived at the time of Emperor Augustus and who is celebrated as a protector of artists. The museum has recently been renovated. The ground floor is organized topographically while the upper floor is organized in specialized sections (paleontology, pre-history, coins, private collections.)