The trainer made his name at Red Star Belgrade before moving onto spells in charge of Yugoslavia and Madrid.
He won back-to-back league titles with the Spanish club in 1975 and 1976, and they posted a message of condolence on their official website.
"Real Madrid wishes to express its deepest condolences to his family. Miljanic left a great impression at the club both professionally and personally," the statement read.
Miljanic also lead the Yugoslav nation to the 1974 and 1982 World Cups.