State media said he had died just after 12:00 local time (04:00 GMT), in Shanghai, on Wednesday.
Jiang presided over a time when China opened up on a vast scale and saw high-speed growth.
His death comes as China sees some of its most serious protests since Tiananmen, with many demonstrating against Covid restrictions.
A Chinese Communist Party statement said he died of leukaemia and multiple organ failure.
It added that he was recognised "as an outstanding leader with high prestige" and "a long-tested Communist fighter".
Some wonder if Jiang's death might trigger more protests in China now - just as the death of former Chinese Communist Party chief Hu Yaobang led to the Tiananmen Square protests 33 years ago.
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