The 75-year-old passed away at 6.15am on Saturday in the Centro de Madrid clinic in the Spanish capital, said the RFEF, who expressed their sorrow at the loss of the "Spain national coach at the start of their glorious run of success in world football."
Spain were long regarded as under-achievers but Aragones changed that perception with the 2008 victory which paved the way for further triumphs under Vicente del Bosque at the 2010 World Cup and Euro 2012.
Aragones realised the need to get rid of old players in the Spain dressing room like Raul and Michel Salgado and create a new playing style based on the short-passing football that was bringing success at Barcelona.
The often eccentric coach was derided in the Spanish press for dropping the established stars before results started to improve. He chose to stand down after the Euro success and then went on to coach Turkish side Fenerbahce which ended in failure after one season in 2009.
Rafa Benitez, who currently manages Napoli in Italy, led the tributes to the former Spain coach.
“I have just heard the news of the sad passing of Luis Aragonés this morning in Madrid,” wrote Benitez on his official website.
“Both as a player and coach was one of the great football legends. He was a reference point for many generations of football players, Coaches and fans of our sport.
“My condolences and thoughts are with his family, friends, colleagues and fans. Rest in peace, the great ‘wise man of Hortaleza’.”
Current Spain coach Vicente Del Bosque added: "It is a sad day for Spanish football. We have lost a key man in the history of our sport.”