Diack led the IAAF from 1999-2015 but was later found guilty of running a clique that covered up Russian doping in return for millions of dollars.
A French court sentenced him to four years in prison in 2020, but he was never jailed.
He was under house arrest there before being released on bail so that he could return to Senegal.
His son, Papa Massata Diack, said on Friday: “He died at home around 2am of a natural death.”
Papa Massata was at the heart of the scandal but fled to Senegal. He was tried in absentia and given a five-year jail sentence.
“With the death of Lamine Diack, Senegal loses one of its most illustrious sons,” Senegal president Macky Sall said on Twitter.