Di Stefano passes away following heart attack
Di Stefano, who celebrated his 88th birthday on Friday, was taken to the intensive care unit at Madrid's Gregorio Maranon Hospital on Saturday and was reported to be in a critical condition.
News of Di Stefano's death was published on Real's official website on Monday.
The statement read: "Real Madrid CF announces that its honorary president, Alfredo Di Stefano, died today at 17:15 [CEST] at the Hospital General Universitario Gregorio Maranon in Madrid.
"The president of Real Madrid, Florentino Perez, and the club's board would like to express their deepest condolences and all their love and affection to his children, family and friends.
"Real Madrid CF extends condolences to those Madridistas around the world and those who feel emotion over the loss of the best player of all time."
The legendary former forward is widely regarded as one of the game's greatest-ever players and made his name during an 11-year spell at Real.
He played an integral role as the Madrid giants won the European Cup five years in a row from 1956 to 1960, and also won the Spanish title eight times. In addition, he was named European footballer of the year in 1957 and 1959.
The Argentina-born forward represented his country of birth, Spain and Colombia at international level, although his appearances for Colombia were not officially recognised by FIFA.