State TV in Saudi Arabia has announced King Abdullah has died after ruling as king for ten years. He was 90.
The report said Abdullah died on January 22, but offered few other details.
Abdullah had been in hospital for several weeks suffering from a lung infection.
He is due to be buried in Riyadh later on January 23.
His successor is his 79-year-old half-brother, Prince Salman, who recently has taken on the ailing Abdullah's responsibilities.
King Salman has named his half-brother Muqrin as his crown prince and heir.
Saudi Arabia holds more than a fifth of the world's crude oil, and also exerts some influence over the world's 1.6 billion Muslims through its guardianship of Mecca and Medina, Islam's holiest sites.
World leaders have been expressing their condolences.
U.S. President Barack Obama saluted the late king's commitment to close U.S.-Saudi ties.
"As a leader, he was always candid and had the courage of his convictions," Obama said in a statement.
Obama, who visited with the ailing king in his desert compound last March, praised Abdullah for taking "bold steps" in advancing the Arab Peace Initiative.
The Saudi-brokered plan was endorsed by the Arab League in 2002, and spelled out steps to end the Palestinian-Israel conflict, most notably offering Arab recognition of Israel's right to exist in exchange for Israeli withdrawal from all land captured since 1967.
A strong U.S. ally, Abdullah sought to modernize the ultraconservative Muslim kingdom with incremental but significant reforms, including offering some more opportunities for women.
Abdullah tried to shape the Middle East, countering rival, mainly Shi'ite Iran wherever it tried to make advances.
He and fellow Sunni Arab monarchs also staunchly opposed the Middle East's wave of pro-democracy uprisings, seeing them as a threat to stability and their own rule.
Abdullah 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.