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 this goal 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."
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."