Reggiani attended the Regio Istituto di Belle Arti di Modena from 1911 to 1916, where he first enjoyed a more general education before concentrating on sculpture. He was drafted into military service in August 1917 while he was still a student and began his pilot's training at the pilot's school in Caserta near Naples in 1918. He completed his studies of sculpture during his military service in 1919. After his return to Modena in 1920 Reggiani began his series of portraits. He moved to Milan in 1924 where he joined the circle around the artist group "Novecento" and exhibited his first works at the Biennale in Venice in 1926. Works of his were on show at various exhibitions during the 1930s, the most important of which was the "Prima mostra collettiva di arte astratta" in 1935. He accepted a teaching post at the Scuola Superiore degli Artefici dell'Accademia di Brera from 1935 to 1946, which was interrupted by his participation in the Second World War. The air raids on Milan on 13th August 1943 also destroyed his studio with 200 works. Reggiani became assistant professor of painting at the Accademia di Brera in 1946, a post that he held until 1955. During the early 1950s he was a member of the "Movimento Arte Concreta (MAC) which had been founded in 1948 in Milan. He frequently exhibited together with this group. Numerous exhibitions in Italy and abroad during the 1960s and 1970s were dedicated to the artist who was celebrated as one of the most important representatives of Italian abstract and concrete art. Reggiani died on 20 May 1980 in Milan.