The club said in a statement that Di Stefano, its honorary president, died on Monday afternoon at Gregorio Maranon hospital, two days after a heart attack.
Di Stefano turned 88 on Friday. The following day, he had a heart attack on a Madrid street near the club's Santiago Bernabeu Stadium. Paramedics were able to resuscitate him after 18 minutes, but he spent the following days in a coma.
Renowned for his speed, versatility and strategic grasp of the game, he helped Madrid attain five straight European Champions Cups and was voted European player of the year in 1957 and '59.
In a career spanning five clubs in three countries - Argentina, Colombia and Spain - from 1945-1966, Di Stefano scored 789 goals in 1,090 matches. In the process he claimed top-scorer status once in the Argentine league, twice in Colombia's league and five times in Spain.
"I'm very saddened by the news of the death of Alfredo Di Stefano," said Sepp Blatter, president of the sport's international governing body. "He was the most complete player I've ever seen. He was also my favorite player."
Those who knew him recall a straight-talking character who believed success on the field came through physical effort and dedication.
"I don't want to be idolized, I just want to play. And to do that you have to run and sweat," he said. His modesty in the face of overwhelming sporting success won him the admiration of many.
"I think he was one of the greatest, if not the greatest, football player ever," England great Bobby Charlton said.
Born July 4, 1926, in the Barracas suburb of Buenos Aires, near the port where British sailors introduced football to Argentina, Di Stefano learned the game while playing free-for-all soccer in what he called "the academy of the streets."
"In our neighborhood we used to hold major football sessions that went on until it got dark, with everyone playing against each other," he said.
"Pope Francis and I went to the same school," Di Stefano said when Jorge Mario Bergoglio was elected pontiff, adding the two likely played together as children.
Di Stefano's father, Alfredo, the son of an immigrant from the Italian island of Capri, was a loyal fan of River Plate. De Stefano's mother, Eulalia Laulhe Gilmont, was of French and Irish ancestry.
Having trialed successfully for River Plate, he turned professional in 1945, joining Colombia's Millonarios six years later. He won six league titles for the two clubs.
His turn of speed soon had fans chanting, "Help, here comes the jet-propelled 'blonde arrow,'" ("Saeta Rubia," in Spanish) a nickname Di Stefano retained all his life.
He played in Spain for the first time in 1952 and dazzled the crowd at a tournament commemorating Real Madrid's 50th anniversary, a fateful encounter.
Barcelona signed Di Stefano in 1953 after agreeing a transfer with River Plate, but the move was thrown into doubt when Madrid also negotiated his transfer - with Millonarios.
Although the Spanish federation authorized Di Stefano to play half of his four-year contract with each club, Barcelona opted out, alleging pressure from the Madrid-based ruling military dictatorship of Gen. Francisco Franco.
In his first season Di Stefano helped Madrid win its second league title, ending a 21-year drought.
Within three years, he helped Madrid lift its first European Cup by scoring in a 4-3 win over France's Stade Reims.
The arrival at Madrid of Hungarian great Ferenc Puskas in 1958 led to an attacking partnership of dynamic effectiveness which allowed the club to retain the European title through to 1960, a record yet to be beaten.
Di Stefano's last final in 1960 at Glasgow saw possibly his finest match. Before 127,000 fans, he scored three times in Madrid's 7-3 demolition of Eintracht Frankfurt.
The same year, he helped Madrid win the inaugural Intercontinental Cup between European and South American champions with a 5-1 aggregate victory over Uruguay's Penarol.
In his remaining four years at Madrid, Di Stefano helped his team lift a further four league titles.
He topped the Spanish league's scoring standings in five of his 11 seasons with Madrid. He scored 49 times in 58 European matches, a record in the competition that stood for more than four decades.
Di Stefano left Madrid in 1964 to join Barcelona-based Espanyol for a two-year spell before retiring at age 40.
"Football brought me so many beautiful moments. It built my life," said Di Stefano, who was also an Argentina and Spain international. But World Cup glory eluded him. Argentina didn't play in 1950 and '54, while Spain didn't qualify for Sweden in 1958. Di Stefano carried an injury to Chile 1962 and did not play. So, his only international success was a 1947 Copa America victory with Argentina.
In 1963, Di Stefano was held captive by a guerrilla group during Madrid's tour of Venezuela. He was taken at gunpoint from his hotel room by the publicity-seeking National Liberation Army Front and released unhurt two days later.
As a coach, he led Boca Juniors and River Plate to Argentine league titles, and won the European Cup Winners' Cup, the Spanish league title and the Copa del Rey with Valencia. He also managed Madrid between 1982 and 1984.
Madrid appointed Di Stefano honorary president in 2000, named its training complex stadium after him six years later and erected a statue in his honor in 2008.
A diabetic, Di Stefano fought ill-health in old age and underwent a quadruple bypass with a pacemaker implanted in December 2005 after a heart attack.
In May 2013 his children asked a court to rule him mentally incapable after he announced plans to marry a woman 50 years his junior.
"I don't care that my children are against it," Di Stefano, then 86, said of his plans to marry 36-year-old Gina Gonzalez.
His interest in football never diminished. At 86 he still maintained a regular column in Spanish sports newspaper Marca.
In it, he revealed that he had missed Pope Francis' appointment. "I must confess that while everyone else watched the white smoke live," he wrote. "I was, as always, watching a football game."
