"With deep sorrow and pain, the royal court ... mourns the death of The Custodian of the Two Holy Mosques King Fahd due to illness," said an official statement read out on Saudi state television on Monday.
The announcement on television was preceded by recitations from the Quran that interrupted regular broadcasting.
Fahd, who was believed to be 83 and had been in poor health, entered hospital on 27 May with acute pneumonia.
Fahd's half-brother Crown Prince Abdullah, who has been running the kingdom's day-to-day affairs since Fahd suffered a stroke in 1995, automatically becomes king. Defence Minister Prince Sultan will be the new crown prince.
"The royal family members have acknowledged Crown Prince Abdullah as sovereign of the country ... after which the Custodian of the Two Holy Mosques and ruler of Saudi Arabia King Abdullah bin Abdul Aziz chose Prince Sultan as crown prince and the family members acknowledged that," the statement said.
A Saudi official said Fahd's funeral would take place on Tuesday to give time for foreign dignitaries to take part.
Saudi Arabia is the world's biggest oil exporter and is a close ally of the United States.
In the past two years, the kingdom has faced a violent al-Qaida campaign to end seven decades of the royal family's rule in Saudi Arabia, home to two of Islam's holiest places of worship.