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.
96 year old probably hasn’t been making many decisions for himself in recent years, but it’s always good when a communist dies, especially one on the state/power side
https://www.youtube.com/watch?v=PpArES47nOI
RIH!