Sheikh Khalifa was president of the UAE since 2004, but his role had been largely ceremonial since he suffered a stroke in 2014.
His half-brother, Mohamed bin Zayed al-Nahyan, is now in charge of state affairs.
The al-Nahyan family is believed to have a fortune of $150bn (£123bn).
As well as being president of the UAE, Sheikh Khalifa was also the ruler of Abu Dhabi, the oil-rich capital of the seven emirates which comprise the UAE.
News of his death was announced by the official WAM news agency.
The ministry of presidential affairs declared 40 days of mourning with flags at half-mast from Friday, and work was suspended in the public and private sectors for the first three days.
Sheikh Khalifa took over as the UAE’s second president in November 2004, succeeding his father as the 16th ruler of Abu Dhabi.
In the first decade of his rule, he presided over a major restructuring of both the federal government and that of Abu Dhabi.
But after his stroke, he was rarely seen in public, although he continued to issue rulings.
US President Joe Biden paid tribute to Sheikh Khalifa, saying he “was a true partner and friend of the United States”.
“We will honour his memory by continuing to strengthen the longstanding ties between the governments and people of the United States and the United Arab Emirates,” Mr Biden said.
Under the UAE’s constitution, the vice-president Sheikh Mohammed bin Rashid al-Maktoum, ruler of Dubai, will act as interim president.
The federal council, which brings together the rulers of the seven emirates, must meet within 30 days to elect a new president.