Gen. Odierno, whom his predecessor termed as "the perfect man for the job," said he was aware of the tough task ahead in Iraq, despite a recent lull in violence.
Addressing a gathering after assuming the new responsibility, he said the recent security gains in the country are "fragile and reversible."
He called upon the Iraqi people to take charge, as "the struggle is theirs to win."
"Iraq is now a different country from the one I had seen first. However, we must realize that these gains are fragile and reversible," Odierno added.
U.S. Defense Secretary Robert Gates, who unexpectedly flew in Monday to attend the ceremony, said the two generals formed an "incredible team" while implementing the troop surge plan last year.
Presiding over the ceremony, Gates recalled the challenges faced by Gen. Petraeus in one of the most risky foreign security missions carried out by U.S. armed forces.
"Darkness had descended on this land. Merchants of chaos were gaining strength. Death was commonplace. Slowly, but inexorably, the tide began to turn. Our enemies took a fearsome beating they will not soon forget," Gates said.
He reminded Gen. odierno to be cautious at a "pivotal moment, when progress remains fragile."
Gen. Petraeus paid tribute to the American soldiers in the fight against terrorism in Iraq.
Gen. Petraeus, who successfully sought the "surge" of nearly 30,000 extra U.S. troops in Iraq, is widely credited with reducing violence there during his 20 months in command.
After putting him at the helm of the Multi-National Force - Iraq in February 2007, the Bush administration heavily relied on Gen. Petraeus in the implementation of its so-called surge strategy.
Since then, the security situation has improved markedly, with less violence and fewer deaths, and progress on both the political and economic fronts of the country.
Petraeus has subsequently been promoted to oversee operations in the Middle East, Afghanistan, and Central Asia.
He will take up the post as 'Commander-in-Chief of the US Central Command next month, working from its headquarters in Tampa, Florida.
U.S. President George W. Bush gave an upbeat assessment of the security gains made in Iraq in July, which witnessed the least number of US troop casualties in the country since the beginning of the war in 2003.
He also announced the shortening of tours of duty in the war-torn country.
Only thirteen U.S. soldiers were killed while in action in Iraq in July, which is a marked reduction from 137 deaths in November of 2004, the highest death toll reported during the five years of US fighting there.
The first half of 2007 was the most violent period of the entire war for the Americans, as 565 of their troops died. The trend has reversed since July last year, however, as the death toll never crossed three digits.
Bush said that he expects commanders in Iraq to suggest "further reductions in our combat forces, as conditions permit."
However, according to a report from the Government Accountability Office released in July, conditions in Iraq remain "volatile and dangerous."
After five years in Iraq, the U.S. military has suffered over 33,000 casualties, with more than 29,000 wounded and 4,000 dead.
Although the reduction in violence helped the Bush administration justify its persistent stand not to shift the focus from Iraq despite criticism, it remains engulfed by obstacles, including reaching a troops withdrawal deal with the Iraqi government, the battle for political control, and leaving a country without solving its civil strife.
It remains to be seen how self-sufficient the Iraqi forces will be in tackling security challenges once the U.S. forces leave the country.
Radical anti-American Shiite cleric Moqtada al-Sadr ordering his militant Mehdi army to lay down arms was a significant development in August. But recurring incidents of suicide bombings, the latest in Diyala province Monday killing 22 people, serve as a reminder that violence could easily escalate again in Iraq.
The big challenge for Gen. Odierno will be finding ways to stop that sort of violence at a time when the number of U.S. troops is being decreased.
Gen. Odierno, who served as deputy commander in Iraq for 15 months, echoed Gen. Petraeus's concerns about Iran, saying the Islamic Republic was the most serious long-term threat to Iraq.
In an interview with the BBC, Gen. Petraeus said he would never declare victory in Iraq and that the U.S. still faced a "long struggle" in that country.
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