King Salman has named his half-brother Muqrin as his crown prince and heir.
"His Highness Salman bin Abdulaziz Al Saud and all members of the family and the nation mourn the Custodian of the Two Holy Mosques King Abdullah bin Abdulaziz, who passed away at exactly 1 a.m. this morning," said the statement.
Abdullah, thought to have been born in 1923, had ruled Saudi Arabia as king since 2006, but had run the country as de facto regent for a decade before that after his predecessor King Fahd suffered a debilitating stroke.
At stake with the appointment of Salman as king is the future direction of the United States' most important Arab ally and self-appointed champion of Sunni Islam at a moment of unprecedented turmoil across the Middle East.
Abdullah played a guiding role in Saudi Arabia's support for Egypt's government after the military intervened in 2012, and drove his country's support for Syria's rebellion against President Bashar al-Assad.
King Salman, thought to be 79, has been crown prince and defense minister since 2012. He was governor of Riyadh province for five decades before that.
By immediately appointing Muqrin as his heir, subject to the approval of a family Allegiance Council, Salman has moved to avert widespread speculation about the immediate path of the royal succession in the world's top oil exporter.
LONG TERM CHALLENGES
Abdullah pushed cautious changes in the conservative Islamic kingdom including increased women's rights and economic deregulation, but made no moves towards democracy and was a hawk on policy towards rival Iran.
King Salman has been part of the ruling clique of princes for decades and is thought likely to continue the main thrusts of Saudi strategic policy, including maintaining the alliance with the United States and working towards energy market stability.
During his five decades as Riyadh governor he was reputedly adept at managing the delicate balance of clerical, tribal and princely interests that determine Saudi policy, while maintaining good relations with the West.
In the long term Saudi rulers have to manage the needs of a rapidly growing population plagued by structural unemployment, and an economy that remains overly dependent on oil revenue and undermined by lavish subsidies.
Saudi Arabia, which holds more than a fifth of the world's crude oil, also exerts some influence over the world's 1.6 billion Muslims through its guardianship of Mecca and Medina, Islam's holiest sites.
Most senior members of the ruling al-Saud family are thought to favor similar positions on foreign and energy policy, but incoming kings have traditionally chosen to appoint new ministers to head top ministries like oil and finance.
In a country where the big ministries are dominated by royals, successive kings have kept the oil portfolio reserved for commoners and insisted on maintaining substantial spare output capacity to help reduce market volatility.
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