After beginning his career with Budućnost Titograd, Savićević moved to Red Star Belgrade, and was a part of the team that won the 1990–91 European Cup, coming second in the 1991 Ballon d’Or, before joining Italian club A.C. Milan in 1992. With Milan, he won three Serie A titles and the 1993–94 UEFA Champions League, among other trophies. He later returned to Red Star for half a season in 1999, before ending his career with Rapid Wien in 2001. At the international level, he represented Yugoslavia at the 1990 and 1998 FIFA World Cups and, after his retirement from playing, coached the Serbia and Montenegro national team between 2001 and 2003. Following an illustrious professional playing career that lasted 18 seasons, as well as a short and unsuccessful head coaching stint during the early 2000s, he has turned to administrative matters – becoming, during the summer of 2004, the president of the Montenegrin FA.