Antic had a varied playing career as a defender spanning 17 years in which he played for Partizan Belgrade in his home country, Fenerbahce in Turkey, Real Zaragoza in Spain before ending his career in England with Luton Town.
He coached a host of Spanish sides including Zaragoza, Real Madrid and Barcelona but is best remembered at Atletico, where he spent five years and led a team containing current coach Diego Simeone to win a La Liga and Copa del Rey double in 1996.
He also led Serbia to qualify for the 2010 World Cup, then going on to work in China. His last stint as a coach was with Chinese Super League side Hebei China Fortune Hebei Fortune in 2015.
"Today we have lost a great person and one of the architects of that magnificent golden age for Atletico. I feel very proud to have known him and shared every moment by his side," said Atletico president Enrique Cerezo.
Real Madrid captain Sergio Ramos also paid tribute, writing on Twitter: "You made Atetico great and you made our rivalry greater. Farewell to a unique coaching career -- Atletico Madrid, Barcelona and Real Madrid. Rest in peace." (Reporting by Richard Martin, editing by Pritha Sarkar)