Aragones was a prominent figure within the national game and led Spain to victory at Euro 2008, beating Germany in the final before ending a four-year spell at the helm.
He was also a successful coach at club level most notably with Atletico Madrid, leading them to the La Liga title in 1977 as well as three Copa del Rey trophies.
A statement from the RFEF read: "The Spanish Football Federation wants to express its grief and shock at the death of Luis Aragones, former player and coach of several Spanish and global clubs and the Spain national team at the beginning of their glorious success on the worldwide stage.
"Luis Aragones led the Spanish team to victory in the 2008 European Championships. He died today in Madrid Clinic, where he had been admitted."
Reports in the Spanish media said Aragones was admitted to the Madrid clinic in the early hours of Saturday morning but died soon after.
Atletico posted a tribute to their former coach on their official website, and will mark his death with a minute's silence ahead of the Primera Division clash with Real Sociedad on Sunday.
"One of the greatest Rojiblancas legends has left us," read the statement.
"There have been condolences from around the footballing world. Our president, Enrique Cerezo, expressed his sorrow saying: 'Luis Aragones was a great player and coach, but above all a great person and a friend. On behalf of the whole club, I want to express our condolences to his family'.
"The club have decided to hold a minute's silence in his memory ahead of the next match against Real Sociedad, in which the players will also wear black armbands in his honour."
Aragones made his name as a player with Atletico between 1964 and 1974, making more than 350 appearances, winning three league titles and also representing Spain 11 times before hanging up his boots.
He then took up the reins with the Madrid club, the first of four spells at the helm in which he led them to six trophies and promotion from the Segunda Division in 2002.
Aragones also guided Barcelona to Copa del Rey success during his one season in charge of the Catalan club in 1987/88.
He then took charge of the national team in 2004, leading Spain to their first major title in 44 years at Euro 2008, the start of a hat-trick of tournament triumphs that continued under his successor Vicente Del Bosque at the 2010 World Cup and Euro 2012.
An ill-fated spell at Turkish side Fenerbahce followed, which came to an end in the summer of 2009, before Aragones officially announced his retirement in December last year - four years after leaving his final coaching post.
As well as his achievements at club and national level, Aragones will also be remembered for the media storm he caused in October 2004 after allegedly making racist remarks about former Arsenal striker Thierry Henry.
Aragones was apparently trying to motivate Henry's then Arsenal team-mate Jose Reyes during a training session ahead of Spain's World Cup qualifier against Belgium when the incident occurred.
The Spain boss is alleged to have referred to Henry using racist language and told Reyes that he was the better player of the two.
The comments from Aragones were captured by cameras from TV station Antenna 3, prompting the coach to later issue an apology to the Frenchman.