Shaikh Jaber,79, had been ailing since suffering a brain hemorrhage five years ago.
The Kuwaiti cabinet named the crown prince, Shaikh Saad al-Abdullah al-Sabah, as the new amir. But because he also was in poor health it was believed that Prime Minister Shaikh Sabah al-Ahmad al-Sabah - half brother of the deceased amir - would continue to handle the day-to-day running of the tiny oil-producing Gulf state.
Shaikh Jaber's body, wrapped in Kuwait's flag, made its way with difficulty through the crowd that gathered for the brief ceremony at Sulaibikhat cemetery. The amir was buried in an unmarked grave as members of the ruling family stood by, raising their hands in prayer.
The new amir, who is in his mid-70s, attended the burial in a wheelchair. Jordan's King Abdullah II was among the dignitaries who came to the funeral.
Thousands of Kuwaitis with mournful expressions filled the flat, dusty cemetery. Some women on the edges of the crowd wept.
Crown Prince Shaikh Saad has
been named the new amir
The government announced a 40-day period of mourning and said offices would be closed for three days.
A number of Arab countries, including Jordan, Egypt, Lebanon and Syria, also announced three days of mourning and lowered their flags in Shaikh Jaber's honour.
Egyptian President Hosni Mubarak described the late amir as "a kind brother and a dear friend".
Jordan's royal court issued a statement of condolences and said the king and his family "will stand by the brothers in the state of Kuwait to overcome this great loss".
"The Arab and Islamic nations have lost a wise leader who consecrated his life to the service of his country, his Arab nation and the Islamic nation," Arab League
Secretary-General Amr Moussa said in a statement.
There had been speculation among Kuwaitis that the crown prince, named heir apparent in 1978, might give up his position because of his health, but the prime minister announced last November that would not happen.
The new amir, a cousin of Shaikh Jaber named his heir apparent in 1978, is in his mid-70s and has colon problems. He travels abroad frequently for medical treatment.
Abdul-Rhida Asiri, head of the Political Science Department at Kuwait University, said the prime minister would be chosen crown prince and most probably keep his present job. "The de facto ruler will be Shaikh Sabah," he told The Associated Press, and the family could make further leadership decisions after the mourning period.
Shaikh Jaber was a close friend of America even before US forces led the fight to liberate his country in 1991. He proved that friendship by supporting the American-led invasion of Iraq 12 years later.
Kuwait has remained reliant on US forces for defence, and the close alliance is likely to continue under Shaikh Saad. Washington named Kuwait a major non-Nato ally in 2004.
The al-Sabah family has ruled this small state that has the world's 10th largest oil reserves - some 95 billion barrels - for more than 250 years. Kuwait is a major member of the Organisation of Petroleum Exporting Countries.
Prime Minister Shaikh Sabah is
expected to be the de facto ruler
After a Shia Muslim extremist tried to assassinate Shaikh Jaber in a suicide car bombing in May 1985, the amir abruptly changed his habits. He stopped driving his own car to bustling bazaars and cut down on public appearances. He did not like travelling abroad, though he went for medical treatment.
He suffered a brain haemorrhage in 2001 and was treated in London. On the rare occasions since then when he appeared in public, he had difficulty delivering speeches.
Shaikh Jaber, born in 1926 before Kuwait became rich exporting oil and educated by private tutors in his father's palace, was considered a father figure to many Kuwaitis.
Despite the wealth and well-consolidated family rule, Shaikh Jaber was considered a quiet listener who avoided ostentation. His palace in Kuwait City's Dasman neighbourhood near the sea was described as a spacious but ordinary house, and bread and yogurt often satisfied him at mealtime.
Designated crown prince and prime minister in 1965, Shaikh Jaber succeeded his uncle, Shaikh Sabah al-Salem al-Sabah, as amir on 31 December 1977.
The year before taking over, he set up the Fund for Future Generations - a financial safety net for Kuwaitis when the oil eventually runs out. To this day, he has ensured that 10% of oil revenues go into the fund, which has an estimated balance of more than $60 billion.
Shaikh Jaber won the praise and gratitude of human rights activists when he decreed in 1999 that women should have the vote and be eligible to run for office. However, conservatives and fundamentalists formed a parliamentary alliance that repeatedly kept his decree from being put into practice.
Six years later, in May 2005, parliament finally approved the legislation supported by the amir.