He played for the national sides of both Uruguay and Italy during his career. He also played for the club sides of the Peñarol and Danubio in Uruguay and A.S. Roma and A.C. Milan in Italy.
Roberto Muylaert compares the black and white film of Ghigghia's cup winning goal in 1950 with Abraham Zapruder's chance images of the Kennedy assassination in Dallas. The goal and the shot that killed the US President have "the same dramatic pattern ... the same movement ... the same precision of an unstoppable trajectory. They even have the dust in common that was stirred up, here by a rifle and there by Ghiggia's left foot." Given the goal cost Brazil a World Cup title at home, Ghigghia would later mention that "only three people managed to silence the Maracanã: Frank Sinatra, the Pope, and me."
On 29 December 2009, Brazil honoured Ghiggia by celebrating his decisive goal in the 2–1 Uruguay victory over Brazil in the final match of the 1950 FIFA World Cup. So Ghiggia returned to Maracanã Stadium almost 60 years later for this honour and planted his feet in a mould to take his place alongside greats including Brazil's Pelé, Portugal's Eusébio and Germany's Franz Beckenbauer at the Maracanã Stadium walk of fame. Alcides Ghiggia was very emotional and thanked Brazil for the warm reception and recognition even when the game is remembered as the most disappointing match in Brazilian football history known as "Maracanazo."
Ghiggia lived his last years at his home in Las Piedras, Uruguay. He died on 16 July 2015 in a private hospital in Montevideo at the age of 88. Coincidentally, it was the 65th anniversary of the "Maracanazo". At the time of his death, Ghiggia was the oldest living World Cup champion.
Ghiggia was the last member from either the Brazilian or Uruguayan squads involved in that 1950 World Cup's historic game to be alive.