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He was the nephew of Anselmo Govi, a painter from Reggio Emilia, who painted the fresco of the dome of the Teatro Ariosto. He belonged to a local Northern Italian aristocratic family previously known as Benedelli. He was the cousin of Emidio Benevelli, the founder of Benevelli Transaxles.
Since 1957 Benevelli exhibited in Italy and worldwide. His first US exhibition was in 1963 at the Felix Landau Gallery in Los Angeles. In 1964 he was invited to the 42nd Venice International Art Biennale with a group of sculptures. In 1966 he was appointed as head of the sculpture courses at the Accademia di Brera in Milan. Between the late 1960s and the early 1970s he created a series of lamp-sculpture, the most famous is the Roto lamp (1970s) and Arabesque (late 1960s). In 2009 he started a collaboration with the worldwide design and furniture brand Natuzzi in the newly created Natuzzi Open Art, a space dedicated to the collaboration between art and design. Benevelli created a new line of art-objects which first premiered at the Cologne Trade Fair (imm Cologne Furniture and Design fair), Salone del Mobile (Milan International Design Fair) and at the AD Home Show in New York (2010).
He realised a number of sacred art works for contemporary and ancient churches, and his works are preserved in numerous public and private collections in Italy and worldwide including at the Royal Museum of Fine Arts in Antwerp and at The British Museum in London.
- Dalla Pietra all’Ago, Rizzoli, 1983
- Tre scultori di Milano, Kenjirō Azuma, Giacomo Benevelli, Giancarlo Marchese, 196?
- Azuma, Benevelli, Marchese: Galleria Mosaico, Chiasso, La Galleria, 1966
- Benevelli: sculture e disegni : Castello di Sartirana (Pavia), [2 giugno - 9 settembre 1990] Ed. "Centro Studi", 1990
- Sculture contemporanee nello spazio urbano: Kengiro Azuma, Iginio Balderi, Giacomo Benevelli, Gianfranco Pardi, Giò Pomodoro, Carlo Ramous, Mauro Staccioli. July 1973, Tipo-lito Nuova Step
- Giacomo Benevelli: forme, Andrea B. Del Guercio, editor S. Benevelli, Photography Cristina Cocullo, Translator R. A. Landon, Casa del Mantegna, 2000, ISBN 978-88-7943-022-7
- "Arte in Italia, 1945–1960", Luciano Caramel, Vita e Pensiero, 1994, ISBN 978-88-343-4885-7