Abdullah bin Abdulaziz was the fifth of his brothers to take the throne and became king in 2005, reports Caroline Hawley
Saudi King Abdullah bin Abdulaziz has died, royal officials have announced, weeks after he was admitted to hospital.
King Abdullah, who was said to be aged about 90, had been suffering from a lung infection.
A statement early on Friday said his 79-year-old half brother, Salman, had become king.
King Abdullah came to the throne in 2005 but had suffered frequent bouts of ill health in recent years.
King Salman had recently taken on the ailing monarch's responsibilities.
Before the announcement, Saudi television cut to Koranic verses, which often signifies the death of a senior royal.
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 01:00 this morning," the statement said.
Frank Gardner says Saudi Arabia could face an increasing internal security problem following the death of King Abdullah
Following tradition, King Abdullah will be buried later on Friday in an unmarked grave.
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.
UK Prime Minister David Cameron said King Abdullah would be remembered for his "commitment to peace and for strengthening understanding between faiths".
Jordan's King Abdullah II cut short a visit to Davos, Switzerland, to travel to Saudi Arabia, as Jordan's royal court declared 40 days of mourning.
Source: BBC