Amadei was born in Frascati, near Rome, the son of a baker, which earned him the nickname "Fornaretto." He made his professional debut on 2 May 1937 with A.S. Roma aged 15 years and 280 days (the youngest debut in Serie A history; surpassed on 12 May 2021 by Wisdom Amey) in a 2–2 draw against Fiorentina. A week later he scored in a 5–1 defeat to A.S. Lucchese Libertas 1905 on 9 May 1937, making him the youngest scorer in Serie A history, a record he holds to this day. He also played in Serie B with Atalanta B.C., Inter and S.S.C. Napoli. He won one Italian title with Roma in the 1941–42 season; this was the club's first ever championship. With A.S. Roma he played 386 matches and scored 101 goals in the Italian top flight, as well as 11 in the Coppa Italia in 18 appearances, 16 goals in eight appearances in the 1944 Campionato Alta Italia, and 15 goals in 34 appearances in the 1945–46 Italian Football "After War" Championship; in his entire career he played 423 matches and scored 174 goals in Serie A, with a total of 508 appearances and 209 goals coming in league play.