Born in Zürich, Burri studied at the Kunstgewerbeschule, about which he was later to make a film. He became an associate member of Magnum in 1955 and a full member in 1959. He was instrumental in creating Magnum films in 1965. He was elected European vice-president of Magnum in 1982 and inaugurated Galerie Magnum in Paris with the exhibition Terre de Guerre, co-curated with Bruno Barbey.