The Argentina-born star passed away in a Madrid hospital on Monday, two days after suffering a heart attack.
Born in 1926, Di Stefano helped transform Real Madrid from serial underachievers into a side that dominated Spanish and European football during the 1950s and early 1960s.
Known as the 'Saeta Rubia' - the Blond Arrow - he helped the club win five successive European Cups between 1956-60 and scored in each of the finals.
Back in 2009 Pele said: "People argue between Pele or Maradona. For me, Di Stefano is the best. He was much more complete."
A Real Madrid statement read: “President Florentino Perez, and the club's executive committee, would like to express their most sincere condolences, love and support for his children, family members and friends," before adding he was "the best player of all time".
During a 21-year playing career, Di Stefano started out with River Plate in Argentina before moving to Europe to join Real Madrid with whom he enjoyed great success.
Although he never appeared in a World Cup Finals tournament, he represented his native Argentina six times, wore a Colombia shirt on four occasions and earned 31 caps for Spain.
Di Stefano scored 789 goals in 1,090 matches. In the process he was top scorer once in the Argentine League, twice in Colombia's league and five times in Spain. He scored 305 goals in 392 matches for Real - second only to Raul in the club's history - and 18 of those came in El Clasico matches.
A two-time European Footballer of the Year, he retired in 1966 before moving into management with a number of clubs, including Real Madrid on two occasions (1982-84, 1990-91).
Sir Bobby Charlton said: "I was deeply saddened to hear the news of Alfredo’s passing. As one of the stars of the legendary Real Madrid team, I think Alfredo Di Stefano was one of the best players I ever came across and an extremely intelligent footballer.
“He was somebody I really respected, having watched him from the stands at the Bernabeu and then played against him.
“I have many fond memories of my time with Alfredo and feel privileged to be able to call him a good friend. The footballing world has lost a great player and a great man.
"I'd like to send my condolences on behalf of everybody at Manchester United to his family and our friends at Real Madrid.”
Spanish state secretary for sport Miguel Cardenal said: "There was nobody who stood comparison. He laid the foundations of a team that was named the best of the 20th century and that this year won the European Champions League.
"The legacy he left in Real Madrid's DNA was of fighting to the end and never giving up. Don Alfredo was the greatest."
FIFA president Sepp Blatter said: “I'm very saddened by the news of the death of Alfredo Di Stefano. He was the most complete player I've ever seen. He was also my favourite player."
Pele said: "Today the openness between Latin American players and European clubs is very much due to the work of Alfredo Di Stefano. He was a trailblazer and most of all he was a legend of the game. God rest his soul."
Chelsea boss Jose Mourinho said: "This is a very sad day for football when we lose a special person like this. Alfredo was the best Real Madrid player in history and one of the greatest of all time."
Argentina superstar Lionel Messi said: “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.”
UEFA president Michel Platini added: "He won everyone's hearts with his brilliance as part of the legendary Real Madrid team that left its indelible mark on European football. He was superb technically, possessed outstanding speed, and was a splendid goalscorer."
Probably the one player you would always point to from that age to demonstrate how much not appearing in a World Cup can dent a public reputation. Shame, but clearly a giant of the game that, hopefully, will inspire documentaries so we can all learn more about his career.- plughead80