Ghiggia suffered a heart attack on Thursday on the 65th anniversary of the famous victory.
Uruguay’s triumph – the second in their history after winning the inaugural competition in 1930 – denied glory to the hosts Brazil, who only needed to earn a draw in the match.
Ghiggia was the victorious team’s last surviving player.
“He came in with a sore back and they hospitalised him,” his son, Arcadio, told a Uruguayan television station. “He was talking to me about football and suddenly he stopped. They tried to revive him but to no avail.”
In the infamous final it was the hosts Brazil who took the lead through a Friaca goal, but a Schiaffino equaliser paved the way for 23-year-old Ghiggia to score the winner 11 minutes from time – muting a capacity crowd of 174,000 at the Maracana.
“It was the first time in my life that I heard something that wasn’t noise,” Schiaffino once said of his team-mate’s goal. “I felt the silence. It felt like everything had ended.”
Ghiggia began his career at the Sudamerica club before moving Uruguay giants Penerol.
His good form in South America didn’t go unnoticed and he soon earned a move to Europe, playing for Roma and Milan before eventually ending his career back in his homeland with Danubio.
In later years Ghiggia became an icon for Uruguayans who admired his quiet grace.
In 2013 he was given a standing ovation by 60,000 fans before Uruguay played Jordan in a World Cup play-off and he was also invited by FIFA to help with the draw for the 2014 tournament in Brazil.
Former Uruguay captain Diego Lugano tweeted his condolences.
“July 16 had to be the day that Alcides left us,” he said.“Thank you for watering out soil with glory. You will be remembered for all eternity. Safe travels champ!”