A statement early on Friday said his half brother, Salman, had become king.
Before the announcement, Saudi television cut to Koranic verses, which often signifies the death of a senior royal.
King Abdullah, who was said to be aged about 90, had been in hospital for several weeks suffering from a lung infection.
Abdullah came to the throne in 2005 but had suffered frequent bouts of ill health in recent years.
King Salman, 79, had recently taken on the ailing monarch’s responsibilities.
The late king’s half brother Muqrin, who is in his late 60s, has been named the new crown prince, the official statement said.
The BBC’s Frank Gardner says Saudi Arabia could face an increasing internal security problem following the death of King Abdullah
All three are sons of the founder of modern Saudi Arabia, King Abdulaziz, usually referred to as Ibn Saud, who died in 1953.
King Salman called on the royal family’s Allegiance Council to recognise 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 1am this morning,” the statement said.
US President Barack Obama expressed his personal sympathies and those of the American people, on the death of King Abdullah.
“As a leader, he was always candid and had the courage of his convictions. One of those convictions was his steadfast and passionate belief in the importance of the US-Saudi relationship as a force for stability and security in the Middle East and beyond,” he said.
Vice-President Joe Biden tweeted that he would lead a delegation to Riyadh to pay respects.
Former President George H.W. Bush also released a statement calling Abdullah “a wise and reliable ally, helping our nations build a strategic relationship and enduring friendship,” according to CBS News.
Messages came in from other leaders around the world, with British Prime Minister David Cameron and Indian Prime Minister Narendra Modi both expressing regret at Abdullah’s demise. Cameron, who visited Saudi Arabia in 2012, said he was “deeply saddened” and expressed hope that the “long and deep ties between our two Kingdoms will continue,” while Modi took to Twitter to commemorate “an important voice who left a lasting impact on his country.”
Abdullah’s spearheading of the Arab Peace Initiative, which was cited by both Obama and U.S. Secretary of State John Kerry as one of his key achievements, was also included in U.N. Secretary General Ban Ki-Moon’s condolence message as “a tangible legacy that can still point the way towards peace in the Middle East.”
Abdullah was the 13th of the 37 sons of King Abdulaziz. He is believed to have been born in August 1924 in Riyadh, although there is some dispute about his actual birth date.
In 1962 he was appointed commander of the Saudi National Guard, where he earned the respect and loyalty of the desert tribes.
When he came to the throne in 2005 he succeeded another half-brother, Fahd.
However, he had already been Saudi Arabia’s de-facto leader for 10 years because his predecessor had been debilitated by a stroke.
Correspondents say Abdullah was seen as a reformer at home, albeit a slow and steady one.
He allowed mild criticism of his government in the press, and hinted that more women should be allowed to work.
King Salman spent 48 years as governor of Riyadh Province before becoming crown prince and defence minister.