Mugabe died in Singapore, where he has often received medical treatment in recent years, a source with direct knowledge of the matter told Reuters.
"It is with the utmost sadness that I announce the passing on of Zimbabwe's founding father and former President, Cde Robert Mugabe," a post on Mnangagwa's official presidential Twitter account said.
In November, Mnangagwa said Mugabe was no longer able to walk when he had been admitted to a hospital in Singapore, without saying what treatment Mugabe had been undergoing.
Officials often said he was being treated for a cataract, denying frequent private media reports that he had prostate cancer.
Mugabe, who ruled the southern African nation for nearly four decades since independence from Britain in 1980, was forced to resign in November 2017 after an army coup.
He was feted as an African liberation hero and champion of racial reconciliation when he first came to power in a nation divided by nearly a century of white colonial rule.
Chain pays tribute to 'outstanding' leader
One of the staunchest supporters of Mugabe, Beijing paid tribute to him, saying he was an "outstanding national liberation movement leader and politician".
"Mugabe was an outstanding national liberation movement leader and politician of Zimbabwe," said Foreign Ministry spokesman Geng Shuang at a press briefing in Beijing.
"Throughout his life, he has firmly defended the sovereignty of his country, opposed foreign interference, and actively promoted China-Zimbabwe and China-Africa friendship and cooperation," said Geng.
Relations between China and Zimbabwe date back to the liberation struggle of the 1960s, when Beijing provided arms and trained some of the top guerrilla leaders.
Beijing remained one of Mugabe's most powerful allies and a major trade partner, even as the West shunned him.
China has funded and provided loans for many infrastructure projects across Africa in recent years, including the new parliament building in Zimbabwe.
Last year President Xi Jinping greeted Mnangagwa as an "old friend" of China when the African leader visited Beijing.