Sultan, whose age was officially given as 80 and who died in New York of colon cancer early on Saturday Saudi time, had been a central figure in Saudi decision-making since becoming defense minister in 1962 and was made crown prince in 2005.
Saudi analysts predicted an orderly transition at a time when much of the Middle East is in turmoil after mass uprisings against autocratic leaders by citizens demanding democracy.
Saudi King Abdullah reacted to the "Arab Spring" by ordering spending of $130 billion on social benefits, housing and jobs, but he and his new crown prince face challenges from al Qaeda militants, a restless Shi'ite minority and civil conflict in neighboring Yemen.
Saudi Arabia is also locked in a confrontation with Shi'ite Muslim power Iran, accused by the United States of plotting to kill the kingdom's ambassador to Washington.
Earlier this month, the Saudi Interior Ministry accused an unnamed foreign power, widely assumed to mean Iran, of instigating protests by the Saudi Shi'ite minority in which 14 people, including 11 security officers, were injured.
Sultan's health had declined in recent years and he spent long periods outside the kingdom for medical treatment. A 2009 U.S. diplomatic cable released by WikiLeaks described him as "for all intents and purposes incapacitated."
King Abdullah is now likely to summon the untested Allegiance Council of the ruling al-Saud family, set up in 2006 to make the succession process more transparent, to approve his preferred heir. In the past, the succession was decided in secret by the king and a coterie of powerful princes.
Most analysts believe the new crown prince will be Nayef, who was appointed second deputy prime minister in 2009, a position usually given to the man who is third-in-line to rule.
"The problem is (the Allegiance Council) is a secret organization that consists of members of the royal family and Saudi society has no say," said Madawi al-Rashid, author of A History of Saudi Arabia and critic of the ruling family. "Some sections of Saudi Arabia are worried. Nayef is known for security solutions. His rhetoric always invokes the sword."
Nayef has been interior minister since 1975 and has managed the kingdom's day-to-day affairs during the absences of both the king and crown prince.
He has gained a reputation as being more conservative than either King Abdullah or Sultan, with close ties to the country's powerful Wahhabi clergy. But as king he might follow a more moderate line in keeping with the al-Saud tradition of governing by consensus, analysts say.
"The succession will be orderly," said Asaad al-Shamlan, a political science professor in Riyadh. "The point of reference will be the ruling of the Allegiance Council. It seems to me most likely Nayef will be chosen. If he becomes crown prince, I don't expect much immediate change."
"Things are in order, thanks to the wise leadership represented in King Abdullah bin Abdulaziz," Prince Talal bin Abdulaziz, a brother of both Abdullah and Sultan and member of the Allegiance Council, told reporters.
When the Allegiance Council convenes, the 34 branches of the ruling family born to the kingdom's founder King Abdulaziz Ibn Saud will each have a vote to confirm the king's nominee for crown prince or appoint their own candidate.
Saudi television broke its normal schedule early on Saturday to broadcast Koranic verses and footage of pilgrims circling the Kaaba in Mecca, Islam's holiest site, before announcing the crown prince's death.
"With deep sorrow and sadness the Custodian of the Two Holy Mosques King Abdullah bin Abdulaziz mourns the death of his brother and his Crown Prince Sultan... who died at dawn this morning Saturday outside the kingdom following an illness," said a Saudi royal court statement carried on official media.
The Saudi stock market was unaffected by the news, and the TASI all-share index closed nearly half a percent up. Shops, schools and universities were open as normal in Riyadh.
Funeral services for Sultan, who died on Friday New York time, will be held on Tuesday in Riyadh. An official at the Saudi embassy in Washington confirmed that Prince Sultan had died in New York but declined to give further details.
U.S. Secretary of State Hillary Clinton expressed her condolences over the death, saying U.S.-Saudi ties are strong.
"The Crown Prince was a strong leader and a good friend to the United States over many years, as well as a tireless champion for his country," Clinton said during a visit to Tajikistan, in the first official U.S. comment on his death.
"Our relationship with Saudi Arabia is strong and enduring and we will look forward to working with the (Saudi) leadership for many years to come," she told a news conference.
Kuwait, Jordan, Morocco, Qatar, Turkey and Oman sent messages of condolence.
King Abdullah, who is in his late 80s, underwent back surgery earlier this month but has been pictured since then in apparently good health.
"The stability of Saudi Arabia is more important than ever," said Turad al-Amri, a political analyst in Saudi Arabia. "All the countries around it are crumbling. The balance of power is changing in the Middle East."
Abdullah has gained a reputation as a cautious reformer since becoming de facto regent of the conservative Islamic country in 1995 and as king since 2005.
He was absent for three months in late 2010 and early 2011 following treatment for a herniated disc that caused blood to accumulate around his spine.
Unlike European monarchies, the line of succession does not move from father to eldest son, but down a line of brothers born to the kingdom's founder Ibn Saud, who died in 1953.
Sultan's death also means King Abdullah will have to select new defense and aviation ministers, key posts in a country that spends billions of dollars on weapons procurement.
Prince Khaled bin Sultan, the son of the late crown prince, has been deputy defense minister since 2001 and is one candidate to replace his father as minister.
"There traditionally has been a way of balancing the power relationships within the family that are important," said Robert Jordan, U.S. ambassador to Riyadh from 2001-03. "So I don't think we should automatically assume that Khaled bin Sultan will become the defense minister, although he has much experience and his father was in place for many years."