As with previous successions, the selection process is likely to be smooth, with King Abdullah and a family council expected to start work on the appointment of a new crown prince swiftly.
Nayef's most likely successor is the pragmatic Prince Salman, 76, a brother of King Abdullah who was made defence minister in November after more than five decades as Riyadh governor, analysts and diplomats in the kingdom said.
The new crown prince will become heir to a king who is 89 years old in a country that faces a range of tough long-term challenges at home and turmoil in the region.
Saudi policymakers are grappling with the threat from al Qaeda, unrest among minority Shi'ite Muslims and youth unemployment.
Meanwhile they are engaged in a rivalry with regional powerhouse Iran as they navigate the aftermath of last year's Arab uprisings including revolts in Bahrain and Yemen, both on their doorstep.
"With deep sorrow and grief ... King Abdullah mourns his brother ... Crown Prince Nayef who passed to the mercy of God on Saturday outside the kingdom," said a royal court statement.
A source close to the royal family said Nayef had died suddenly in Geneva after receiving treatment for a knee complaint. He was thought to be 78.
U.S. President Barack Obama issued a statement of condolences, saying that under Nayef's leadership, "the United States and Saudi Arabia developed a strong and effective partnership in the fight against terrorism, one that has saved countless American and Saudi lives."
The U.S. embassy in Riyadh said Washington had "lost a close friend".
The death was not expected to trigger any major changes to the kingdom's energy policy or to key relationships with the United States and other allies.
"The fundamental principle that the Saudis operate under is stability," said Robert Jordan, U.S. ambassador to Riyadh from 2001-03. "So they will, I'm sure, develop a consensus among the senior members of the family over an orderly succession. That has likely been forming in recent months in any event."
At stake is the future direction of a country that possesses more than one fifth of proven global oil reserves.
Seen as a key ally for the West, Saudi Arabia has provided critical intelligence to foil al Qaeda plots, bankrolled pro-Western Arab governments and has supported Washington's attempts to isolate Iran.
To liberals, Nayef, a son of the state's founder, was the forbidding face of a conservative establishment that opposed any real moves toward democracy or greater women's rights, oversaw the fearsome religious police and took a hard line against members of the Shi'ite Muslim minority.
A 2009 assessment of Nayef made by the U.S. embassy and released by WikiLeaks said he "displays signs of personal prejudice against the Shia".
On his watch, the conservative kingdom emerged from last year's Arab uprisings looking like one of the most stable states in the Middle East.
"He supervised the security affairs of the state for more than 30 years. He scored a lot of successes there. Especially in fighting al Qaeda," said Khalid al-Dakhil, a Saudi analyst.
Analysts said Nayef's death meant King Abdullah was likely to call on the family Allegiance Council, which he formed in 2007, to affirm his choice of a new crown prince, probably in the coming days.
"Salman will take over as crown prince and it will be seamless. I don't see any major ramifications," said Theodore Karasik, a security analyst for the Dubai-based INEGMA group.
Since King Abdullah is already 89, his crown prince would probably assume a major role in state affairs quickly.
As Riyadh's governor for five decades, Nayef gained considerable experience dealing with foreign diplomats, tribal leaders and important clerics, three important constituencies for any Saudi leader.
"It appeared to me he had a good handle on the delicate balancing act he had to do to move society forward while being respectful of its traditions and conservative ways," said former Ambassador Jordan.
Saudi Arabia does not practice official mourning periods or close government offices after the death of a senior royal.
However, when Crown Prince Sultan died last October there was a three-day condolences period when foreign dignitaries and tribal and religious leaders paid their respects to King Abdullah before his new heir was announced.
After Nayef's death, state TV played Koranic verses and aired footage of pilgrims circling the great mosque in Mecca, Islam's holiest site, where Nayef will be buried on Sunday.
