In September 2020, he was found guilty of corruption and money-laundering, linked to the Russian doping scandal.
A French court sentenced him to four years in prison, two of them suspended.
He was never jailed and allowed to return to Senegal, where he remained under house arrest and was later released on bail.
“He died at home of a natural death,” his son, Papa Massata Diack, said.
His funeral is due to be held later on Friday.
Diack’s lawyers had previously said he was in poor health and would die if sent to prison.
Despite his conviction he still enjoyed support in Senegal with Cheikh Seck, the owner of Senegalese football club Jaraaf, paying a 500,000 euro ($565,000 or £425,000 bond earlier this year that allowed Diack to return home.
“He was a good man, a great leader. We wanted him to come back home. It took us one month (to gather the 500,000 euros),” Seck, a businessman and former Senegal international goalkeeper, said after Diack’s death.
“It was really important, we never imagined he could finish his life somewhere else.”
In the past Seck described Diack as: “A worthy son of the nation, an all-round remarkable citizen.” Bbc
