The Supreme Court has been asked to find a replacement to Conte, who was a reclusive diabetic and chain-smoker, and 40 days of national morning have been declared.
The former colonial solider led the world's number one bauxite exporter with strong arm tactics since taking power in a coup in 1984, after Sekou Toure, the West African country's first president, died in a US hospital.
He had won three sets of elections in the country post-1993. However, the polls were mostly boycotted by opposition groups who said that they were undemocratic.
Conte had failing health since the 2002, occasionally falling into a coma, generating rumours of his death.
This led to campaigning on a reduced scale in presidential elections in 2003, but he neverthless won with over 95 per cent of the vote.
Opposition parties increasingly called for Conte - who was frequently abroad in Morocco, Switzerland and Cuba for medical treatment later on during his presidency - to step down, raising fears of political instability should he die while in power.
Demonstrations against his rule in 2007 and last month were suppressed in deadly fashion, with 186 and 4 people being killed respectively.
However, he was defiant concerning his position towards the end of his reign.
"I am the boss, others are my subordinates," he said in 2007.
"There is no question of transition," he said, after being questioned about who might take over from him.
After the country gained independence from French rule in 1958, Conte climbed through the army's ranks to deputy head, before being chosen to lead a so-called Military Recovery Committee that overthrew the government, promising civilian rule and democracy.