Abdullah, who had ruled since 2005 and was aged 90, had been suffering from a lung infection.
His 79-year-old half-brother, Salman, has been confirmed as the new king.
Within hours of his accession to the throne of the oil-rich kingdom, King Salman vowed to maintain the same policies as his predecessors.
"We will continue adhering to the correct policies which Saudi Arabia has followed since its establishment," he said in a speech broadcast on state television.
Abdullah had suffered frequent bouts of ill health in recent years, and King Salman had recently taken on the ailing monarch's responsibilities.
Prior to announcing Abdullah's death, Saudi television cut to Koranic verses, which often signifies the passing of a senior royal.
In line with traditions of Wahhabism - the ultra-conservative form of Sunni Islam followed by the kingdom - Abdullah will be buried in an unmarked grave today, Friday, January 23, 2015.
- BBC News