Tancredi Parmeggiani was born in Feltre, Belluno, on 25 September 1927. He studied at the Accademia di Belle Arti in Venice and in 1946 became friends with Emilio Vedova. In 1947 he made a trip to Paris and in the following two years he spent his time between Feltre and Venice, where he held his first solo exhibition at the Galleria Sandri in 1949. In 1950 he moved to Rome, where he joined the Age d'Or group, which organised exhibitions and publications of the international avant-garde.
In 1951, he participated in an exhibition of Italian abstract art at the Galleria Nazionale d'Arte Moderna in Rome. In the same year he settled in Venice, where he met Peggy Guggenheim, who offered him a studio in her palace and organised an exhibition for him in 1954. In 1952, he received the Premio Graziano for painting in Venice. In the same year he signed the manifesto of Spatialism, the movement founded by Lucio Fontana around 1947.
He exhibited in solo shows at the Galleria del Cavallino in Venice in 1952, 1953, 1956 and 1959, and at the Galleria del Naviglio in Milan in 1953. In 1954 he participated with Jackson Pollock, Wols, Georges Mathieu and others in the exhibition 'Tendances Actuelles' at the Kunsthalle Bern. In 1955 he exhibited in a group show at the Galerie Stadler in Paris, a city that Tancredi visited in the same year. In 1958 he held solo exhibitions at the Saidenberg Gallery in New York and the Hanover Gallery in London, and participated in the Carnegie International in Pittsburgh. He moved to Milan in 1959, where he exhibited several times at the Galleria dell'Ariete. Again in 1959 he went to Paris; in 1960 he was in Norway and took part in the 'Anti-Procès' exhibition at the Galleria del Canale in Venice, where he also had two solo exhibitions in 1960 and 1962. In 1962 he received the Marzotto Prize, in Valdagno, and in 1964 he exhibited at the Venice Biennale. He died by suicide in Rome on 27 September 1964.