On his Twitter account, his family and the Kofi Annan Foundation said he died peacefully on Saturday after a short illness.
Annan, who was chairman of the foundation, left behind a wife, Nane, and children named Ama, Kojo and Nina, who were by his side on his last days.
The family said: "Annan was a son of Ghana and felt a special responsibility towards Africa.
"He was particularly committed to African development and deeply engaged in many initiatives, including his chairmanship of the Africa Progress Panel and his early leadership of the Alliance for a Green Revolution in Africa (AGRA)."
The Ghanaian was key to the peace deal that was struck in Kenya after the 20077/8 post-election violence.
The peace accord signed between retired President Mwai Kibaki and Opposition leader Raila Odinga ended the violence that was sparked by a disputed election.
It saw the birth of the Grand Coalition Government with Kibaki as the President and Raila as the Prime Minister.
Annan described his chief mediator role as the most engaging but noted that it ended a stalemate that left at least 1,000 people dead.
"My role in mediating was amongst the most intensive and enduring of all my interventions," he said in March 2017, nine years after the process.
Annan was the first black African to take up the role of the world's top diplomat, serving two terms from 1997 to 2006.
He later served as the UN special envoy for Syria, leading efforts to find a peaceful solution to the conflict.
His tenure coincided with the Iraq War and the HIV/Aids pandemic.