A hero of the all-conquering Real sides of the 1950s and 1960s, the striker known as the "Blonde Arrow" is ranked alongside Pele, Maradona and Johan Cruyff — though unlike them he missed out on World Cup glory.
Announcing his death on Monday, Real Madrid called the Argentine-born Di Stéfano, its honorary club president, simply "the best player of all time".
"Alfredo Di Stéfano changed the history of this club and he changed the history of football," the club's chairman Florentino Perez told a news conference.
"He has left us, but his legend will live forever."
Di Stéfano had gone into a coma after suffering a heart attack on Saturday at a restaurant near Real's Santiago Bernabeu stadium.
He died on Monday at 5:15 pm (1515 GMT) at the Gregorio Marañón hospital, Real Madrid said in a statement.
"Real Madrid extends its condolences to its fans around the world and to those who are feeling the emotion of losing the best player of all time."
Di Stéfano had previously been hospitalized for similar episodes and underwent emergency quadruple heart by-pass surgery after a heart attack in 2005.
A player capable of disorienting dribbles, pinpoint passes and a lethal threat in front of goal, Di Stéfano combined technical and tactical skill with an irrepressible spirit.
A football match without goals "is like a Sunday without sunshine", went one of his best-known sayings.
He was a two-time European Football of the Year in 1957 and 1959, but never made it to the finals of a World Cup.
Argentina did not play in the 1950 and 1954 finals and having obtained Spanish citizenship in 1956 Di Stéfano missed out on the 1958 finals as Spain failed to qualify.
Spain reached the 1962 tournament in Chile but injury prevented Di Stéfano, then aged 35, from taking part.
He was one of Real Madrid's most celebrated players, however, representing the club for 11 seasons between 1953 and 1964, winning five European Cups.
Di Stéfano was born in Buenos Aires and began his professional career with hometown club River Plate in 1945 before leaving for Colombian outfit Millonarios four years later.
He soon attracted the attention of various big European clubs.
Legends never die
After a long transfer wrangle with Barcelona, it was arch-rivals Real Madrid who won the race for Di Stéfano's signature.
He helped Real Madrid end a 21-year wait for the league title in his first season and added a further seven league crowns.
However, it was on the European stage that Di Stéfano truly cemented his status as one of the game's greats.
He helped Real win the first five editions of the European Cup between 1956 and 1960, a record that stands to this day.
Tributes and condolences poured in on Monday from sporting personalities around the world and clubs including Barcelona.
The president of world football's governing body FIFA, Sepp Blatter, called Di Stéfano "the most complete player I've seen".
Others to remember him included Spain's national coach Vicente del Bosque and striker Gonzalo Higuain, who scored Argentina's goal in their 1-0 World Cup quarter-finals win over Belgium on Saturday.
Real Madrid's current star striker Cristiano Ronaldo called it "a very sad day. For me, for all the Madridistas, for the world of football", in his own Twitter message.
"Don Alfredo leaves us, but his memory will last forever in our hearts. Legends never die. Thanks for everything Maestro."
Perez said Di Stéfano's body would lie in state in the Bernabeu from 0830 GMT on Tuesday, as the deceased himself requested.
"This stadium was his factory, his sacred ground, his home and his life," Perez said.