The former Spain player and Atletico Madrid legend died in the Spanish capital's Clinica Cemtro in the early hours of Saturday morning, local time.
After a career in football spanning six decades, Aragones had only confirmed his retirement in December last year.
Atleti president Enrique Cerezo said in a club statement: "Luis Aragones was a great player and coach, but before all that, a great person and a friend.
"He was Atletico above all. I want to express our condolences to his family on behalf of the club."
A striker in his playing days, 'The Sage of Hortaleza' was best known for a 10-year spell with Atleti in which time he won La Liga three times, as well as the Pichichi award for being the Spanish top-flight's top scorer in 1970.
However, they would return rejuvenated in Austria and Switzerland two years later, beating the likes of Russia, Italy and Sweden on their way to the showpiece where Fernando Torres' goal was enough to seal a 1-0 win over Germany and Spain's first major honour since the 1964 European Championships.
Spain remain a powerhouse of world football and are strong favourites for this year's World Cup in Brazil, having reached last year's FIFA Confederation Cup final - losing to the South American nation.
