Earlier, in his inaugural address, Mr Obama made reference to the scale of his achievement at being the first black American elected to the White House, in a remark that gathered one of the biggest cheers of the speech.
"This is the meaning of our liberty and our creed... why a man whose father less than 60 years ago might not have been served at a local restaurant can now stand before you to take a most sacred oath."
The new president takes office amid a dismal economic climate and with the US still embroiled in two wars.
"Our nation is at war, against a far-reaching network of violence and hatred. Our economy is badly weakened," he said, blaming the current situation both on the greed of a few and the "collective failure" of many.
He branded healthcare "too costly", said schools "fail too many" and charged that US energy policy both strengthens enemies and threatens the planet.
"The challenges we face are real," Mr Obama said. "They are serious and they are many. They will not be met easily or in a short span of time.
"But know this America - they will be met."
Invoking the memory of the US's Founding Fathers, Mr Obama said he would strive to rebuild his nation's standing in the world, saying: "We are ready to lead once more."
He addressed the foreign policy challenges facing the US, saying the US would "responsibly leave Iraq to its people and forge a hard-earned peace in Afghanistan".
Crowds at the inauguration of Barack Obama describe their experiences
The new president also addressed the world's poor and the Muslim world, much of which angrily opposed the actions of the previous administration.
From now on, Mr Obama said, the US would seek "a new way forward, based on mutual interest and mutual respect".
The BBC's Kevin Connolly, in Washington, says Mr Obama delivered a difficult inaugural message.
Its task, our correspondent notes, is to lift hopes and hearts at a moment when every economic indicator is falling.
On a day of unprecedented security in Washington DC, the inauguration ceremony began on the West Front Lawn of the US Capitol, where Congress sits, with an opening prayer asking for the protection and safety of the new president and vice-president.
US BLACK HISTORY MILESTONES
1861 - Civil war starts
1865 - Civil war ends, leading to abolition of slavery
1870 - Hiram Revels is first African-American senator. African-American men gain the vote, but face resistance and intimidation
1954 - Civil disobedience campaign starts
1963 - Martin Luther King: "I have a dream" speech
Mr Obama - introduced to the crowd as Barack H Obama - stood solemnly during the invocation by conservative Rick Warren, his eyes closed in the final moments before he took office.
Aretha Franklin then sang against a backdrop of clear blue skies and a light wind. Thousands waved flags as the soul legend sang to a rapturous reception.
Joseph Biden, a veteran senator, was then sworn in as vice-president by the longest-serving member of the US Supreme Court.
The focus then shifted to America's first black president.
Using his full name, Barack Hussein Obama, he placed his hand on a Bible used by Abraham Lincoln at his inauguration in 1861 and repeated the oath of office, promising to "preserve, protect and defend the Constitution of the United States".
Hundreds of thousands of visitors had arrived in Washington in the days before the inauguration, and vast numbers braved early-morning cold to secure a vantage point for the midday ceremony.
Competition for tickets along the parade route was fierce, as was the scrum for standing room in the National Mall.
OBAMA'S ECONOMIC CHALLENGE
Unemployment rate up to 7.2% - 16-year high
Retail sales fell for six months in a row in December - down 2.7%
Car sales down to 22.4% below level seen a year ago
New home sales in November at lowest level in 17 years
Mid-price of a new home sold in November: $220,400 (£149,900) - down 11.5% from a year ago
Trade deficit dropped to $40.4bn (£28.82bn) in November - five-year low
Officials in Washington reported record numbers of passengers on the city's subway network early on Tuesday, and police were forced to close a key entry point hours before event began because of overcrowding.
Before the ceremony began, Michelle and Barack Obama attended a private church service at St John's Episcopal Church alongside Joe Biden and his family.
They then headed to the White House for coffee with outgoing President George W Bush and Vice-President Dick Cheney.
The group - including Mr Cheney in a wheelchair after pulling a back muscle - then left for the US Capitol.
Mr Bush has now left Washington by helicopter bound for Midland, Texas, before heading to the family ranch at Crawford.
Mr Obama and his wife, by contrast, have a series of lavish inaugural balls to attend.
1. 1700GMT/1200EST Obama is inaugurated as US president on the West Front Lawn of the Capitol building 2. Obama escorts former President George W Bush and Vice President Dick Cheney on the presidential procession prior to their departure 3. 1920GMT/1420EST Parade starts along Pennsylvania Avenue 4. Obama will review troops from behind a bullet-proof screen in Lafayette Park, behind the White House 5. President Obama and the First Lady will attend a series of celebration balls, returning to the White House at 0725GMT/0225EST Wednesday
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