Stars pay tribute to Di Stefano
Di Stefano, who turned 88 last Friday, was taken to Madrid's Gregorio Maranon Hospital following a heart attack on Saturday.
News of his passing was reported by Real earlier on Monday.
The Argentine-born forward is one of the most decorated players in the history of football, and scored in every final as Real won the European Cup five years in a row from 1956 to 1960.
He scored 308 goals in 396 competitive appearances for Real, and won the Ballon d'Or award in 1957 and 1960.
Many footballing luminaries have taken to social media to pay their respects to Di Stefano, with FIFA president Sepp Blatter leading the tributes to the iconic figure on Twitter.
"Sad to learn of Di Stefano's passing, the most complete player I’ve seen," he wrote. "My favourite player. A legend is gone. RIP."
Current Real star Cristiano Ronaldo and head coach Carlo Ancelotti were also among those to mourn Di Stefano's passing.
"It's a very sad day. For me, for all the Madridistas, for the world of football," Ronaldo tweeted. "Don Alfredo leaves us, but his memory will last forever in our hearts. Legends never die. Thanks for everything maestro."
Ancelotti added: "I would like to take this opportunity to give my condolences to the friends, family and Real Madrid supporters. Today left a great role model, however his legacy in both life and football will remain in our hearts forever."
Barcelona and Argentina star Lionel Messi wrote on Facebook: "The world lost a legend today, Don Alfredo Di Stefano. An amazing man on and off the field. My thoughts are with his family and friends."
As well as Argentina, Di Stefano also represented Spain and Colombia on the international stage, although FIFA did not recognise his appearances for the latter.
The Spanish Football Federation (RFEF) released a statement reading "Official communication: The RFEF regrets the loss of Alfredo Di Stefano", while the Argentina Fooball Association commented: "Farewell, master Alfredo Di Stefano."
Real's La Liga rivals Atletico Madrid and Barcelona offered their condolences, while the wider footballing community - including the likes of Manchester United, Liverpool, Milan and Chelsea - also paid their respects.
Bobby Charlton, England's record goalscorer and United legend told his club's official website that the "footballing world has lost a great player and a great man", and Barcelona president Josep Maria Bartomeu added: "With Di Stefano's farewell we lose one of the football greats."
Barca and Spain playmaker Andres Iniesta tweeted "Rest in peace Alfredo Di Stefano. Football legend", and Uruguay international Luis Suarez labelled Di Stefano a "genius of football".