The announcement further said King Abdullah's brother, former Crown Prince Salman bin Abdulaziz, has been declared the King.
"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.
King Abdullah, who was in his 90s, had been suffering from a lung infection for several weeks at the hospital.
He had been in bad health for the last few years.
The passing away of the senior royal, who took the throne in 2005, was marked with Quranic verses on Saudi television.
An official statement also said the late monarch's half brother Moqren has been named the new crown prince.