The prominent Quranic figure died in a hospital in the northern city of Erbil after a long illness.
His body has been taken to the city of Ramadi in central Iraq for burial, according to Qaaf news agency.
Born in 1941, al-Daylami started learning the Quran by heart at an early age and managed to become a memorizer in two years.
He then began to learn Quran recitation and soon become a famous Qari.
Quranic activities are very common in the Arab country and have been growing since the 2003 overthrow of former dictator Saddam Hussein.