Grondoma got sick early Wednesday morning and was taken to hospital having been suffering from heart problems and died while undergoing emergency surgery.
The all-powerful figure, who had been in charge of Argentine football since 1979, was reported dead at around 1pm.
He had earlier in the week held meetings with Alejandro Sabella, who decided not to continue as Argentina coach after leading the team to the World Cup final in Brazil.
Grondona had been a FIFA Executive member since 1988 and was appointed to the head of AFA nine years earlier by the country’s military government.
He had been successfully re-elected by clubs to continue governing football in the South American nation every four years since 1979.
His time in charge saw Argentina win the World Cup in Mexico in 1986, the Copa America in 1991 and 1993 and Olympic gold in 2004 and 2008.
AFA’s Vice-President, Luis Segura; Second Deputy President, Juan Carlos Crespi and Director General of National Teams, Carlos Bilardo approached the Sanatorio Mitre private medical center as news about Grondona’s death was confirmed.