Vedova was born in Venice into a working-class family. After an initial formative experience within Expressionism, he joined the group "Corrente" (1942-43), which included other artists such as Renato Guttuso and Renato Birolli. He participated in the Resistenza and played a key role in the post-war Italian art movement, which was opening up and contributing originally to the European avant-garde. In 1946 he co-signed the manifesto of the Fronte Nuovo delle Arti, which included several Italian artists who were to become famous. In 1952 he became a member the influential Gruppo degli Otto (Afro, Birolli, Corpora, Santomaso, Morlotti, Vedova, Moreni, Turcato), organised by the critic Lionello Venturi. His work exerted a significant influence on the Arte Povera group.
He later established a fruitful cooperation with composer Luigi Nono, designing scenographies and costumes for the opera Intolleranza (1960). In 1984 he designed a highly original light setting for Nono's opera Prometeo at La Fenice. Nono dedicated to Vedova his first work for magnetic tape Omaggio a Vedova(1960).
Vedova spent most of his life in Venice, where he taught at the Accademia di Belle Arti from 1975 to his death; his wife Annabianca predeceased him a month earlier.