Iraqi Prime Minister Nuri al-Maliki said Hussein's death "ends a dark chapter" in the country's history.
Reports from Iraq say hundreds of people went to Hussein's gravesite today to pay respects to the former strongman.
The London-based human rights group Amnesty International, which has long campaigned for the abolition of the death penalty, says it "deplores" the execution, which it says followed an "unfair trial."
Hussein was convicted and sentenced to death on November 5 for crimes against humanity over the 1982 killings of 148 Shi'as. On December 26, an Iraqi appeals court upheld that verdict and the death penalty.
Hussein was laid to rest in the same family shrine where his sons, Uday and Qusay, were also buried after U.S. troops killed them in mid-2003.
Relatives said the burial ceremony took about 25 minutes. It was attended by the governor of Salaheddin Province, Hamid al-Shakti, and leaders of Hussein's Albu Nasir tribe.
The former Iraqi leader's cousin, Yousif Ali Hussein, was also there. "They brought the president (Hussein) at 3:30 a.m.; the governor and the [U.S.-led] coalition forces came and they made it a condition that he should be buried overnight," he said.
While the former ruler's death closes an era of Iraq's history marked by war with Iran and a 1990 invasion of Kuwait, U.S. President George W. Bush says it will not end the sectarian violence that some say is pushing Iraq toward civil war.
On December 30, car bombs set off by suspected Sunni insurgents killed more than 70 people in Baghdad and near the Shi'ite holy city of Al-Najaf.
'Door Open' To Hussein Supporters
Prime Minister al-Maliki has tried to reach out to Hussein's Sunni supporters. He said the "door is still open" to those with no blood on their hands to help rebuild Iraq.
But Hussein backers appear unlikely to heed his call. In Amman, Jordanian Ba'ath Party members meeting on December 30 said Hussein's death should inspire the resistance in Iraq and elsewhere in the Arab world.
Grainy video footage of the execution, circulating on the Internet today, provided a further glimpse of the depth of the sectarian passions burning in Iraq.
In the footage, Hussein's executioners exchanged taunts with him as they prepared to hang him. They invoked the name of anti-American Shi'ite cleric Muqtada al-Sadr, whose father was killed by Hussein's agents.
"The New York Times" quoted witnesses as saying one of Hussein's masked guards shouted: "You have destroyed us. You have killed us. You have made us live in destitution."
Hussein reportedly countered by saying, "I have saved you from destitution and misery and destroyed your enemies, the Persians and Americans."
Iran is seen the main backer of al-Sadr. In Tehran today, top cleric Ali-Akbar Hashemi-Rafsanjani, leading Eid al-Adha prayers, praised Hussein's death.
"In Iraq, the issue of Saddam's execution was the sign of God's historical justice which was promised to all human beings," Hashemi-Rafsanjani said.
Al-Sadr is the head of a powerful Shi'ite political movement and a militia, the Imam Al-Mahdi Army, blamed by Washington and Sunni Arabs for running death squads targeting Hussein's Sunni Arab community.
Muted Arab Reaction
In the Arab world, most governments have refrained from public comment.
But a senior aide to Arab League Secretary-General Amr Moussa called the execution "a tragic end to a sad phase in Iraq's history."
Libya declared three days of mourning.
"This is an American crime that is added to all contemporary crimes because he is a war prisoner and human rights laws do not allow to surrender him to the hostile party," Meshaan al-Juburi, an Iraqi parliamentarian, told Reuters after news of the execution.
"In addition to that, I think Saddam is going to be a martyr and his execution in this way will deepen the disagreement in Iraq," he said in a reference to Shi'a invocation of the name of the Shi'ite Prophet Husayn. "If the Iraqis are still crying 'al-Husayn' for the last 1,400 years, I think that the same will happen concerning Saddam Hussein. The chances of a national agreement have become very low."