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.
After retiring in 1974, Aragones immediately became Atleti coach, going on to coach at the Vicente Calderon in four separate spells, bringing them back into La Liga after relegation to the Segunda Division in 2000.
As well as his titles with Atleti, he also won the Copa del Rey with Barcelona in 1988 and ended his coaching career with a one-season spell with Fenerbahce in 2008-09.
Having taken the national job in 2004, Aragones kickstarted one of the most dominant eras in international football history.
Spain stumbled in the 2006 FIFA World Cup in Germany, falling in the second round to eventual finalists France.
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.
Aragones stepped aside after that triumph and Vicente del Bosque has gone on to replicate that success, winning the 2010 FIFA World Cup in South Africa, as well as leading La Roja to retaining their European crown in 2012.
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.
Though Spain have gone on to make great strides under Del Bosque, Aragones is credited with taking a vastly talented squad and finally shaking off the failings that had dogged previous squads, instilling a will to win as well as a flowing style of football.