French President Francois Hollande described the late king as "a statesman whose work has profoundly marked the history of his country."
In Britain, Prime Minister David Cameron hailed King Abdullah as a man who strengthened inter-religious dialogue in the world.
"The Kingdom of Saudi Arabia and the Arab nation have lost a prominent leader, who had given a lot to his people and nation," Egyptian President Abdel Fattah al-Sisi said in a mourning statement.
The history will always remember the late king's achievements in defending the causes of Arabs and Islam, the statement added.
Abdullah, born in 1924, was hospitalized in December for pneumonia and had been breathing with aid. He died at 1:00 am Friday (2200 GMT Thursday).
Funeral prayers will be held later in the day following afternoon prayers at Imam Turki Bin Abdullah Grand Mosque in the capital Riyadh.
Former Crown Prince Salman bin Abdulaziz Al Saud received the pledge of allegiance as the country's king from members of the royal family. Afterwards, Prince Muqrin bin Abdulaziz received the pledge of allegiance as the new crown prince.
When it comes to Africa, China's inroads are just getting started