Rounding off his state visit to Britain, the president rejected the argument that the rise of new economic powers such as China had sidelined Europe and America, insisting that "the time for our leadership is now".
At a "pivotal moment" in history, with demands for democracy across the Arab world and an international coalition fighting oppression in Libya, Britain and America remained "indispensable to the goal of a century which is more peaceful, more prosperous and more just", he said.
Mr Obama was speaking to both Houses of Parliament in the historic Westminster Hall shortly after talks with Prime Minister David Cameron at 10 Downing Street.
In a joint press conference, the two leaders agreed that the transatlantic special relationship was now an "essential relationship" for global stability and prosperity.
Insisting there would be "no let-up" for Muammar Gaddafi until he stood aside and allowed the Libyan people to shape their own future, they pledged to "turn up the heat" on Tripoli and other brutal authoritarian regimes.
But they stressed they had "learned the lessons" from military adventures under Tony Blair and George Bush, and were taking action in Libya as part of a wide coalition operating within the terms of a clear UN mandate.
Rather than Blair and Bush, it was Roosevelt and Churchill that Mr Obama evoked as he praised the virtues of the special relationship in his keynote speech at Westminster Hall.
Speaking to an audience including Mr Cameron and former PMs Gordon Brown, Mr Blair and Sir John Major, Mr Obama said he had known "few greater honours" than becoming the first US President to address what he termed "the mother of Parliaments" in the 900-year-old hall.
It is an honour previously granted to only a handful of eminent figures including Nelson Mandela, the Queen and Pope Benedict XVI - a line-up who Mr Obama quipped represented "either a very high bar or the beginning of a very funny joke".
Mr Obama recalled the alliance of Britain and America in the Second World War, the Cold War and the struggle against terrorism as he said: "The reason for this close friendship doesn't just have to do with our shared history, our shared heritage, our ties of language and culture, or even the strong partnership between our governments.
"Our relationship is special because of values and beliefs that have united our people through the ages."
That relationship had seen Britain and America joining forces "from the beaches of Normandy, to the Balkans to Benghazi", said Mr Obama.
And he said that the UK and US had a continued responsibility to stand up for the values of freedom, democracy and universal rights.
"If we fail to meet that responsibility, who would take our place and what kind of world would we pass on?," he asked.
"Our action, our leadership, is essential to the cause of human nature so we must act and lead with confidence in our ideals and an abiding faith in the character of our people who sent us all here today."
The rapid growth of countries such as China, Brazil and India was welcome but did not mean a declining influence for the US and Europe, said Mr Obama.
"Perhaps, the argument goes, these nations represent the future and the time for our leadership has passed. That argument is wrong. The time for our leadership is now."
America, Britain and democratic partners had "shaped a world in which new nations could emerge and individuals could thrive" and remained "indispensable" to a prosperous future.
"Even as more nations take on the responsibilities of global leadership, our alliance will remain indispensable to the goal of a century which is more peaceful, more prosperous and more just.
"At at time when threats and challenges require nations to work in concert with one another, we remain the greatest catalysts for global action.
"In an era defined by the rapid flow of commerce and information, it is our free market tradition, our openness, fortified by our commitment of basic security to our citizens, that offers the best chance of prosperity that is both strong and shared."
Addressing the wave of pro-democracy protests in north Africa and the Middle East, Mr Obama warned: "History tells us that democracy is not easy. It will be years before these revolutions reach their conclusion and there will be difficult days along the way."
But he added: "Make no mistake, what we saw - what we are seeing - in Tehran, in Tunis, in Tahrir Square, is a longing for the same freedoms that we take for granted here at home.
"It was a rejection of the notion that people in certain parts of the world don't want to be free or need to have democracy imposed on them.
"It was a rebuke to the worldview of al Qaida which smothers the rights of individuals and would thereby subject them to perpetual poverty and violence.
"Let there be no doubt, the United States and the United Kingdom stand squarely on the side of those who long to be free."
Earlier, Mr Obama and Mr Cameron rolled up their sleeves to jointly dish out burgers and sausages at a Downing Street barbecue for military families.
The two leaders served the cooked meat at a lunch party while their wives, Samantha and Michelle, spooned side dishes onto guests' plates.
Later, Mrs Obama visited Oxford University's Christ Church college greeting youngsters from Elizabeth Garrett Anderson school. She first met pupils from the north London secondary school two years ago when she paid them a surprise visit during a trip to the capital with her husband.
The trip, which was arranged at Mrs Obama's suggestion, has been designed to teach the girls about university and encourage them to think about studying for a degree.
Mr Obama and Mr Cameron sealed a raft of initiatives to support military veterans, enhance security co-operation and collaborate in hi-tech scientific projects.
They will tomorrow morning travel to France for a summit of the G8 group of major economies.
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