Ben Bella, who had recently been released from a hospital stay for respiratory problems, died at his family home in Algiers, state news agency APS reported.
"Today we lost one of modern Algeria's bravest leaders," said current President Abdelaziz Bouteflika in a message of condolence read on national television.
He declared an eight-day period of national mourning from Wednesday. The funeral will be held Friday at Algiers' El Alia cemetery after 1230 GMT.
A hero of Algeria's independence from France, Ben Bella was president from 1963 to 1965, when he was overthrown by his defence minister, Houari Boumediene, a close ally of Bouteflika.