"With sadness ... the Omani Sultanate court mourns ... our Sultan Qaboos bin Said ... who God chose to be by his side on Friday evening," the agency said.
It added that Qaboos died after "a wise and triumphant march rich with generosity that embraced Oman and extended to the Arab, Muslim and entire world and achieved a balanced policy that the whole world respected."
A three-day period of mourning has been declared in Oman, and the country's flag will be flown at half-mast for a period of 40 days.
Oman's royal family will have to decide in 72 hours who will replace Qaboos.
Qaboos, the longest ruling Arab monarch, had been ill for some time and had been believed to be suffering from colon cancer. He had spent a week in Belgium undergoing medical treatment in early December.
Sultan Qaboos, 79, ruled Oman since overthrowing his father in a bloodless coup in 1970.
Since assuming power, Qaboos transformed Oman from an isolated backwater, with little or no infrastructure, into a modern state.
But his prolonged absence for treatment has stirred questions over succession in the country of 4.5 million people.
He had recently returned to the capital, Muscat, after medical treatment in Germany and Belgium.
Transition of power
In October 2011, Qaboos, who has no children or brothers, amended the process of succession. But he has not publicly announced who that successor would be.
The sultan, whose closest relatives are his cousins, appointed five top officials to a council that would be involved in confirming the new sultan in case of any royal family dispute.
Under Omani law, if the royal family fails to agree on a successor, the position will then go to the person, whose name is in two sealed letters written by Qaboos.
Oman observers say the sultan's three cousins - Assad, Shihab and Haitham bin Tariq al-Said - stand the best chance.
"I imagine that the succession itself will be a smooth process within Oman," Kristian Coates Ulrichsen of the Texas-based Rice University's Baker Institute told Reuters news agency.
"Sultan Qaboos had such charismatic authority and became so synonymous with Oman as a modern nation-state that it will naturally be difficult for any successor to replicate that, at least at the beginning."
Al Jazeera's Diplomatic Editor James Bays, reporting from the United Nations, said the death leaves a political vacuum not just in his country, but also in the region.
"He is a very big loss in the region. Oman played an outsized role in the region, particularly in the Gulf and the wider Middle East," our correspondent, pointing out that Qaboos played a crucial role in secret negotiations leading to the 2015 Iran nuclear deal.
"I think people are worried particularly at this time of turbulence, at a time when relations between the US and Iran are so bad, when in recent days the two countries have seen come so close to war."
Our correspondent also noted that the death of Qaboos comes at a time when the Gulf Cooperation Council has become deeply divided following the Saudi Arabia-led blockade against Qatar.
SOURCE: Al Jazeera and news agencies
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