The al Qaeda leader was shot dead by US special forces who stormed his villa in the Pakistani town of Abbottabad in the early hours of Monday morning local time.
Bin Laden's compound was close to a military garrison and was only around 40 miles from the capital, Islamabad.
Photographs issued by the White House show the president and other members of his team looking tense as they watch live video of the mission as it happened.
US Secretary of State Hillary Clinton is shown with a particularly anxious expression, with a hand clasped over her mouth.
US chief counter-terrorism advisor John Brennan was also among those viewing the footage. He said: "It was probably one of the most anxiety-filled periods of time. It was clearly very tense, a lot of people were holding their breath.
"There was a fair degree of silence as the operation progressed. "Minutes passed like days and the president was concerned about security of his personnel."
He added that a "tremendous sigh of relief" came in response to confirmation that bin Laden was among those found in the compound.
Asked how Mr Obama reacted when he received the news that bin Laden had been killed, Mr Brennan recalled that the president had said "We got him".
Mr Brennan said he would not reveal details "about what types of visuals we had or what type of feeds that were there but it was - it gave us the ability to actually track it on an ongoing basis".The Navy Seal team that carried out the operation were likely to have been wearing helmet cameras that were able to transmit video and sound back to command centres.
One picture shows the president and Chairman of the Joint Chiefs of Staff US Navy Admiral Mike Mullen sharing what appears to be a congratulatory handshake.