Branzi was born in Florence, in 1938 where he also graduated in architecture. His work and interests relate to industrial design, architecture, urban planning, and cultural promotion. He also works as a professor of industrial design at the Politecnico di Milano University.

He founded with Paolo Deganello, Massimo Morozzi and Gilberto Coretti the Archizoom associates. He is a promoter of the Italian Radical Architecture movement. From the Radical Period, came the very famous Superarchitettura theoretical framework, which brought to Anti-Design.

In his career, Branzi wrote many books, among which are 'Learning from Milan', 'The Hot House and Domestic Animals' (published by MIT press),

'Nouvelles de la Metropole Froide' (Centre Georges Pompidou) and 'Introduzione al Design Italiano'.

In 1983 he was one of the founders of the 'Domus Academy', the first international post-graduate school of design.