A statement, made early on Friday, said his 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.
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.
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.
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.
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.
Courtesy of www.bbc.com