The toponym Branzi seems to derive from the dialectal voice Branz, or gallows tooth, a tool used to harvest hay. The first inhabitants of the area seem to have been the Romans, who began to exploit the copper mines present in the territory, as well as in the neighbouring villages (especially Isola di Fondra).
In the 16th century it became part of the Republic of Venice and in this period the mining activity developed further, which flanked copper with iron, and the production of the piodere, the slate stones still used today in the construction of roofs.
The town also gives its name to the typical local cheese, Branzi, used for the preparation of the famous Polenta Taragna.
It is only in the last decades that the tourism industry has begun to gain more and more popularity and the village is recovering after a period of slow and inexorable depopulation.