The Sultan removed his father from office in a bloodless coup with British support in 1970 and set the oil wealth Oman on a path to development.
Widely regarded as popular, he was also an absolute emperor and any dissenting voices were silenced.
No cause of death has been confirmed yet.
His cousin Haitham bin Tariq Al Said has been sworn in as his successor.
The former culture and heritage minister took the oath of office on Saturday after a meeting of the Royal Family Council, the government said.
The sultan is the paramount decision-maker in Oman. He also holds the positions of prime minister, supreme commander of the armed forces, minister of defence, minister of finance and minister of foreign affairs.
Last month Sultan Qaboos who had no heir or designated successor – spent a week in Belgium for medical treatment, and there were reports he was suffering from cancer.
“With great sorrow and deep sadness the royal court mourns His Majesty Sultan Qaboos bin Said, who passed away on Friday,” a court statement said earlier, announcing three days of national mourning.
For almost five decades, Sultan Qaboos completely dominated the political life of Oman, which is home to 4.6 million people, of whom about 43% are expatriates.
At the age of 29 he overthrew his father, Said bin Taimur, a reclusive and ultra-conservative ruler who banned a range of things, including listening to the radio or wearing sunglasses, and decided who could get married, be educated or leave the country.
[The late Oman Sultan Qaboos Bin Said. Photo/courtesy].
Sultan Qaboos immediately declared that he intended to establish a modern government and use oil money to develop a country where at the time there were only 10km (six miles) of paved roads and three schools.
In the first few years of his rule, he suppressed with the help of British Special Forces an insurgency in the southern province of Dhofar by tribesmen backed by the Marxist People’s Democratic Republic of Yemen.
He was described as charismatic and visionary, he pursued a neutral path in foreign affairs and was able to facilitate secret talks between the United States and Iran in 2013 that led to a landmark nuclear deal two years later.
President Uhuru Kenyatta, Mombasa Governor Ali Hassan Joho and Kenyan ambassador to Omar Sheikh Mohammed Dor are among the first people who sent their condolences to the royal family.
[More reports by BBC].