Osama bin Laden's death has been confirmed by DNA tests that show a "virtually 100%" match with the al Qaeda leader, US officials have revealed.
The world's most-wanted man was buried at sea in the early hours of the morning, after he was killed by a gunshot to the head at a villa in the Pakistani town of Abbottabad.
Officials said his body had also been identified by a woman believed to be one of his wives.
US President Barack Obama, who watched the operation unfold in real time on TV screens, said: "The world is safer, it is a better place because of the death of Osama bin Laden."
A US defence official said Bin Laden was given an Islamic funeral, which involved him being wrapped in a white sheet and washed before being sent overboard.
It is being reported that video footage of that ceremony and photographs of the body are likely to be released soon.
Reports have also emerged that a video thought to have been recorded by Bin Laden some time before his death is due to surface in the near future.
US chief counter-terrorism advisor John Brennan insisted Bin Laden would have been taken alive if there had been the opportunity.
That contradicted sources that had previously claimed the operation had been a "kill mission", with no attempt to capture the target.
He also said a woman - thought to be another of Bin Laden's wives - had been killed during the operation after he used her as a human shield.
But he praised Mr Obama's decision-making.
"The president had to evaluate the strength of that information and then made what I believe was one of the most gutsiest calls of any president in recent memory," he said.
CIA director Leon Panetta warned al Qaeda was likely to seek to avenge the death of its figurehead.
"Though Bin Laden is dead, al Qaeda is not," he said.
"The terrorists almost certainly will attempt to avenge him."
Blood-stained carpets, stripped beds and emptied drawers can be seen in footage filmed inside the villa by American broadcaster ABC News following the raid.
Video pictures showed flames rising from the scene of the firefight between US forces and Bin Laden's guards just before 1am local time on Monday.
It is thought the al Qaeda leader had been living in the walled $1m villa - just 37 miles from the Pakistani capital Islamabad - for at least the last eight months.
The high-security luxury home, which was built in 2005, aroused suspicion after authorities noted it had no telephone or internet connections.
Bin Laden's compound is very close to Pakistan's main army training camp - the Pakistani Kakul Academy in Bilal Town.
US officials said the CIA tracked Bin Laden to his location, then elite troops from Navy Seal Team Six, a top military counter-terrorism unit, swooped on the hideout in four helicopters.
The al Qaeda leader, blamed for the 9/11 attacks on America in 2001, was reportedly asked to surrender by US forces before he was shot in the head.
Pakistani television stations earlier broadcast what they claimed was a photograph of the bloodied face of the world's most wanted man after his death, but this was later shown to be a fake.
Officials said one of military helicopters suffered mechanical failure during the operation and was destroyed after troops had safely disembarked, leading to the blaze visible at the scene.
"A small team of Americans carried out the operation with extraordinary courage and capability. No Americans were harmed. They took care to avoid civilian casualties," President Obama said.
Pakistan's High Commissioner in the UK told Sky News the country's authorities had not been aware of Bin Laden's presence in Abbottabad until after his death.
Wajid Shamsul Hasan nevertheless insisted that there was "total cooperation" between Pakistani authorities and the US government.
Following the operation, President Obama confirmed in a news conference: "I can report to the American people and to the world, that the US has conducted an operation that killed Osama bin Laden."
The US president said he was briefed last summer about a possible lead to the whereabouts of Bin Laden - who fled the US-led invasion of Afghanistan in 2001 - and last week appproved an operation "to bring Bin Laden to justice".
Speaking from Downing Street, the Prime Minister David Cameron said the news would be welcomed across the country.
"It is, I believe, a massive step forward," he said.
Meanwhile, the Foreign Office issued an alert to UK nationals overseas, advising them to monitor local reactions and remain vigilant.
Radical preacher Anjem Choudary, who acts as spokesman for Muslims Against Crusades claimed that attacks on the UK and fierce fighting abroad would be sparked within days.
"I think Britain is more likely to face a 7/7 today than ever," the sharia law lecturer said.
Former president George W Bush said it was a "momentous achievement".
"The fight against terror goes on, but tonight America has sent an unmistakable message: No matter how long it takes, justice will be done," he said in a statement.
President Obama also warned that "al Qaeda will continue to pursue attacks" against the US.
And US Secretary of State Hillary Clinton added that the al Qaeda "syndicate of terror" did not end with bin Laden's death.
The US state department issued a worldwide travel alert to all US citizens warning of an "enhanced potential" for US citizens to be targeted.