In a statement today, Obama said that Bin Laden was killed in a "firefight" during a ground operation at a compound outside Islamabad, Pakistan. The AP quoted a US official as saying that Bin Laden's body was buried at sea, although that has not yet been confirmed.
Bin Laden was accused of being behind a number of terrorist atrocities, including the September 11 attacks in 2001 on New York and Washington that left more than 3,000 people dead.
Despite being America's number one terrorist target with a $25m bounty on his head, Bin Laden had evaded the US and its allies for more than a decade.
Hundreds of people gathered outside the White House in Washington DC to celebrate the news. However, the US has put its diplomatic facilities around the world on high alert over fears of al-Qaida reprisals.
The US state department has also issued a worldwide travel alert to all US citizens warning of an "enhanced potential" for them to be targeted.
Obama revealed that the ground operation followed intelligence gained last August on Bin Laden's possible whereabouts.
"I met repeatedly with my national security team as we developed more information about the possibility that we had located Bin Laden hiding within a compound deep inside of Pakistan," he said.
"And finally, last week, I determined that we had enough intelligence to take action, and authorised an operation to get Osama Bin Laden and bring him to justice,"
In a blog posting, David Cameron said that the news of Bin Laden's death will bring "great relief to people across the world".
"Osama Bin Laden was responsible for the worst terrorist atrocities the world has seen - for 9/11 and for so many attacks, which have cost thousands of lives, many of them British," he said.
"It is a great success that he has been found and will no longer be able to pursue his campaign of global terror. This is a time to remember all those murdered by Osama Bin Laden, and all those who lost loved ones."
Former US president George W. Bush added: "This momentous achievement marks a victory for America, for people who seek peace around the world, and for all those who lost loved ones on September 11, 2001.
"The fight against terror goes on, but tonight America has sent an unmistakable message: No matter how long it takes, justice will be done."
The news of Bin Laden's death has already caused a massive surge of activity on social media networks, with many people hearing the news on Twitter before traditional media outlets.
Tellingly, Republican party political strategist Patrick Ruffini wrote: "I'd love to poll the crowd at WH (White House) on how they heard about it: TV or social media?"
Celebrities such as former governor of California Arnold Schwarzenegger, singer Lily Allen and CNN newsman Piers Morgan have also reacted to the news on Twitter.
According to Bloomberg, the oil price dropped the most in two weeks in New York today as traders speculated that Bin Laden's death may ease the risk of Middle East supply disruptions.
However, CNN is reporting that former Pakistan president Pervez Musharraf believes that the US attack on Bin Laden's compound was a "violation" of Pakistan's sovereignty.
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Watch US president Barack Obama address Osama Bin Laden's death below: