Aurelio started his professional career with local Adelaide team Adelaide City before moving to Europe in the mid 1990's to Belgium, where he was the league's top scorer in the 1994-95 season. He also played in Spain, Switzerland, Netherlands and in Japan before returning to Australia in 1999 to rejoin City. Vidmar signed with Adelaide United when they took Adelaide City's spot in the National Soccer League and was awarded the captaincy by then coach John Kosmina. Despite plans to play in the inaugural A-League season he retired in 2005 bringing an end to a 20 year playing career in which time he played 517 games scoring 127 goals.
Vidmar was a member of the Socceroos team for 12 years and was a member of three FIFA World Cup qualification campaigns. He played and scored against Diego Maradona's Argentina in Australia's final qualifying ties in 1993.
After his retirement in 2005 he took up a role of assistant coach working under Kosmina, he was appointed as head coach on May 2, 2007. He created history by leading Adelaide to the 2008 Asian Champions League final, becoming the first Australian team to achieve such a feat. This lead to Adelaide United CEO Sam Ciccarello to re-sign Vidmar and his assistant Phil Stubbins for another 3 years in November 2008.
Vidmar was inducted into the Football Federation Australia Football Hall of Fame in the same month. He is also in the Football Federation of South Australia Hall of Champions.