A statement from the Ministry of Presidential Affairs said it “condoles the people of the UAE, the Arab and Islamic nation and the world over the demise of His Highness Sheikh Khalifa bin Zayed Al Nahyan, the president of the UAE”.
The leader had been battling an illness for several years, state media reported.
The country will now enter 40 days of mourning, a three-day ban on work, and all flags will be flown at half-mast.
Sheikh Khalifa had served as the president of UAE since 2004 after the death of his father.
Born in 1948, he was the second president of the country and the 16th leader of Abu Dhabi.
He had long stopped being involved in day-to-day affairs of ruling the country, with his brother, Abu Dhabi’s Crown Prince Mohammed bin Zayed, seen as the de-factor ruler.
Sheikh Khalifa had rarely been seen in public since 2014 when he had surgery following a stroke.
There was no immediate announcement about his successor – but Mohammed bin Zayed is in line to inherit the top post.
The prince said on Twitter: “The UAE has lost its righteous son and leader of the ’empowerment phase’ and guardian of its blessed journey.”
Condolences have poured in from Arab leaders – including Bahrain’s king, Egypt’s president and Iraq’s prime minister.
The world’s tallest building in Dubai is named the Burj Khalifa after the late ruler – whose oil-rich emirate helped bail Dubai out during a financial crisis.
The Abu Dhabi royal family – which was headed by Sheikh Khalifa – is said to be worth a staggering £120billion.
The Sheikh also chaired the Abu Dhabi Investment Authority which controls assets worth more than £571billion.
His brother, Sheikh Mansour, has amassed a £17billion fortune of his own, mainly thanks to his booming International Petroleum Investment Company.
Under the constitution, vice-president and premier Sheikh Mohammed bin Rashid al-Maktoum, ruler of Dubai, will act as president until the federal council meets within 30 days to elect a new president.