The 88-year-old, whose name is etched into Hampden history through his hat trick in the 1960 European Cup Final, was kept in an induced coma following his admission to General Universitario Gregorio Maranon Hospital on Friday but has since died.
Di Stefano, regarded as one of the greatest players of all time, had health problems in recent years and was fitted with a pacemaker in 2005 after heart surgery.
The Argentina-born forward enjoyed a prosperous footballing career, most notably winning five successive European Cups with Real Madrid between 1956 and 1960, and scoring in all of them.
During his two-year tenure as manager, Real were runners-up in five competitions, including the 1983 Cup Winners' Cup, in which they lost to an Aberdeen side managed by Sir Alex Ferguson.
Former Manchester United manager Sir Alex said: "Di Stefano was one of the greatest in my mind. He had fantastic balance and poise. He was always the focus of Real Madrid wherever they went. He had a fantastic life and I'm proud to have been associated with him in a small way."
However, Scots football fans best remember him for his key role in the famous Real Madrid European Cup win at Hampden.
His Hungarian teammate Fenenc Puskas netted four of Real Madrid's goals in the Spanish side's 7-3 victory over the German champions Eintracht Frankurt watched by 127,621 fans in Glasgow, which remains a record European Cup final attendance.
The Scottish Football Association's own history of Hampden describes the final as one that "many agree was the greatest ever European Cup final".
Former Scotland manager Craig Brown was a 20-year-old wing half with Dundee when he went to see the famous game with others in the team and believes it helped inspire his club.
"I think you could say to further our football education they took us to the game," he said. "It did help, because 18 months later Dundee won the Scottish championship and got to the semi final of the European Cup. It was inspirational to see that performance. I remember one goal, he picked the ball up deep in his own half, and it is unusual for a striker, in that he ran the length of the park and scored, thrashed it in from just outside the penalty box. I don't think I've seen anything like it."
"Obviously, he is a lifelong hero of most Scottish fans. That game at Hampden Park crystallised the affection in which he was held in Scotland. That whole team was legendary throughout the years, but particularly when they came to Hampden."
Andy Cameron, the Scots comedian renowned for his 1978 World Cup anthem Ally's Tartan Army, tweeted: "Sad day for football with the passing of the magnificent Alfredo Di Stefano at 88. Thank you for Hampden 1960. RIP."