King Salman has called on the family's Allegiance Council to pay allegiance to 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 1 a.m. this morning," said the statement.
Abdullah, thought to have been born in 1923, had ruled Saudi Arabia as king since 2006, but had run the country as de facto regent for a decade before that after his predecessor King Fahd suffered a debilitating stroke.
King Salman, thought to be 79, has been crown prince and defence minister since 2012. He was governor of Riyadh province for five decades before that.
By immediately appointing Muqrin as his heir, subject to the approval of a family Allegiance Council, Salman has moved to avert widespread speculation about the immediate path of the royal succession in the world's top oil exporter.
