Mr Mugabe had been receiving treatment in a hospital in Singapore since April. He was ousted in a military coup in 2017 after 37 years in power.
The former president was praised for broadening access to health and education for the black majority.
But later years were marked by violent repression of his political opponents and Zimbabwe's economic ruin.
His successor, Emmerson Mnangagwa, expressed his "utmost sadness", calling Mr Mugabe "an icon of liberation".
Mr Mnangagwa had been Mr Mugabe's deputy before replacing him.
Singapore's foreign ministry said it was working with the Zimbabwean embassy there to have Mr Mugabe's body flown back to his home country.
Who was Robert Mugabe? He was born on 21 February 1924 in what was then Rhodesia - a British colony, run by its white minority.
After criticising the government of Rhodesia in 1964 he was imprisoned for more than a decade without trial.
In 1973, while still in prison, he was chosen as president of the Zimbabwe African National Union (Zanu), of which he was a founding member.
Once released, he headed to Mozambique, from where he directed guerrilla raids into Rhodesia but he was also seen as a skilled negotiator.
Political agreements to end the crisis resulted in the new independent Republic of Zimbabwe.
With his high profile in the independence movement, Mr Mugabe secured an overwhelming victory in the republic's first election in 1980.
But over his decades in power, international perceptions soured. Mr Mugabe assumed the reputation of a "strongman" leader - all-powerful, ruling by threats and violence but with a strong base of support. An increasing number of critics labelled him a dictator.