Brio was born in Lecce, Apulia. He began his career with his local club, U.S. Lecce, during the 1973–74 season, before moving to Juventus for the 1974–75 season, although he did not make a single appearance with the club that season. He was later sent on loan to Pistoiese from 1975 to 1978, before returning to Juventus. His first season with the Turin club was the 1978–79 season, and he made his Serie A debut with Juventus on 18 March 1979, as they defeated Napoli 1–0. He remained with the club until the 1989–90 season, captaining the club from 1989 to 1990, when he retired from professional football. Overall, he made 378 appearances for Juventus in all competitions, scoring 24 goals, 16 of which came in Serie A over 243 appearances. Brio played for Juventus during one the club's most successful periods, forming a formidable defence alongside Dino Zoff, Gaetano Scirea, Claudio Gentile, and Antonio Cabrini, winning four Serie A titles, three Italian Cups, a European Cup, a Cup Winners' Cup, an UEFA Cup, a European Super Cup, and an Intercontinental Cup, under managers Giovanni Trapattoni, and subsequently Dino Zoff.