Upon joining Red Star, he was loaned to FK Rad for the whole 1989–90 season. When Ljupko Petrović became coach of Red Star, Jugović was returned to the starting eleven. In 1991, Jugović played in the 1991 European Cup Final, which Red Star won. Subsequently, he won the Intercontinental Cup as Red Star beat Colo-Colo 3–0. By the end of his career with Red Star, he was awarded the Star of Red Star and became one of the most celebrated footballers in Yugoslavia.
Jugović was bought by Serie A giants Juventus. In two seasons at Juventus, he won an Italian national title, as well as a UEFA Champions League, scoring the decisive penalty in the final game against Dutch side AFC Ajax.