President Donald Trump has painted a bleak picture of a broken country after being sworn in as US president.
He spoke of abandoned factories, rampant crime and a failed education system, pledging that his presidency would bring about change.
"This American carnage stops right here and stops right now," President Trump said on the steps of the Capitol.
Thousands of Trump supporters travelled across the country to witness the occasion from the National Mall.
The moment marks the end of an improbable journey for the property tycoon after a campaign marked by controversy.
Shortly after the ceremony Mr Trump was seen signing his first official actions as the 45th president.
He sent his Cabinet nominations to the Senate as well as a signed a proclamation for a national day of patriotism, according to Press Secretary Sean Spicer.
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He also signed into law a waiver allowing retired Marine General James Mattis, his pick for defence secretary, to serve in the post.
The change of hands was reflected on the White House website, which was scrubbed of Mr Obama's policies and replaced with Mr Trump's new agenda.
The Trump administration has only listed six issues on the website: energy, foreign policy, jobs and growth, military, law enforcement and trade deals.
Critics pointed out the revamped site made no mention of civil rights, LGBT rights, healthcare or climate change.
Mr Trump briefly spoke at a Capitol luncheon to thank his Democratic opponent Hillary Clinton and her husband, former President Bill Clinton, urging them to rise to applause.
In his inaugural address, he promised to be the voice of the "forgotten people", ignored by Washington politicians.
Today, he said, was "the day the people became rulers of this nation again".
"I will fight for you with every breath left in my body and I will never ever let you down," said President Trump after Chief Justice John Roberts administered the oath.
"America will start winning again, winning like never before.
"We will bring back our jobs, bring back our borders, bring back our wealth and we will bring back our dreams."
The big experiment - Anthony Zurcher, BBC News, Washington
If Donald Trump's speech at the Republican National Convention was billed as "midnight in America" - a pessimistic view of the current conditions in the US - then his message on inauguration day was that it's always darkest before the dawn.
In an address that was tonally consistent with candidate Trump's campaign rhetoric, the president railed against a Washington elite that flourished while the American people suffered.
Early reports were that Mr Trump would offer a non-ideological appeal for national unity - and there were motions in that direction at times toward the end of his speech. This address, however, was very much aimed at his supporters - uniting the people with pitchforks against an out-of-touch establishment.
American voters - at least ones in enough states to form an Electoral College majority - have taken a chance on Mr Trump. His presidency will be a remarkable experiment for American democracy, as it's clear after this speech that Mr Trump intends to govern as he campaigned.
The new president has set the stage. He has four years to make his supporters proud and prove all the doubters wrong.
President Trump and Vice-President Mike Pence waved goodbye as the Bidens and Obamas left the Capitol.
The Obamas held hands as they boarded a military helicopter that took them to Joint Base Andrews in Maryland.
Mr Obama delivered remarks to staff and supporters before he and his wife flew to Palm Springs, California, for a holiday.
He told a crowd they "proved the power of hope" and that "this isn't a period, it's a comma in the continuing story of building America".
The transfer of power prompted congratulatory messages for Mr Trump from dignitaries around the world including Pope Francis.
He said he was praying Mr Trump's decisions would be guided by the "rich spiritual and ethical values" that have shaped America's history.
British Foreign Secretary Boris Johnson also offered well wishes, and Canadian Prime Minister said he looked forward to restoring "prosperity to the middle class on both sides of the border".
Former presidents and first ladies, including George W Bush and his wife Laura as well as Jimmy Carter, were in attendance.
The only absences were 92-year-old George Bush Senior, who is in hospital being treated for respiratory problems, and his wife Barbara.
But more than 50 House Democrats had refused to attend the ceremony in protest.
Mr Trump takes power at a time when the country appears to be deeply divided. He enters the presidency with historically low approval ratings.
He has vowed to roll back many of his predecessor's policies, including repealing Mr Obama's signature health care law and building a wall along the US-Mexico border.
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Authorities arrested nearly 100 people protesting against the inauguration, according to the Metropolitan Police Department.
Many were apprehended for "vandalism and destruction of property", said spokesman Lieutenant Sean Conboy.
Earlier, about 150 protesters dressed in black marched through Washington, smashing windows and rolling rubbish bins into the street to form blockades.
The Women's March on Washington on Saturday - for racial and gender equality, and other issues perceived to be under threat from Mr Trump's administration - is expected to draw about 200,000 people.
On the White House petition page, two new requests appeared for the new president.
One petition demanded Mr Trump divest his financial interest or put them in a blind trust and another called for him to release his taxes.
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