"The RFEF is sorry to announce the death of Luis Aragones," read a statement on their website.
"The RFEF wants to express its pain and consternation at the death of a man who was a player and coach at a number of Spanish clubs and around the world, and the Spanish national team coach at the beginning of its most glorious era of success at international level."
As well as the Spanish national side, Aragones managed 10 different clubs during a 35-year coaching career.
"Luis Aragones was a great player and coach, but more than that a great person and friend," said the Atletico president Enrique Cerezo in a statement on the club's website.
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"He was an Atletico man above all else. I want to express on behalf of all those at the club our condolences to the family."
His crowning glory came on the international stage, though, in Austria and Switzerland in 2008 when he guided the until-then perennially underachieving Spanish national side to their first major tournament victory since 1964.