He said he did not feel he deserved to be in the company of some of the "transformative figures" who had previously received the award.
Some of his aims, particularly the goal of universal nuclear disarmament, would be difficult to achieve even within his lifetime, let alone his presidency, Mr Obama said.
And he sought to deflect some of the global surprise at his win, describing the award as "affirmation of American leadership on behalf of aspirations held by people in all nations".
"I know that throughout history the Nobel Peace Prize has not just been used to honour specific achievements," he said.
"It's also been used as a means to give momentum to a set of causes. And that is why I will accept this award as a call to action, a call for all nations to confront the common challenges of the 21st Century."
The White House has said that the cash prize that accompanies the award will be distributed among several charities.
There were a record 205 nominations for this year's peace prize. Zimbabwean Prime Minister Morgan Tsvangirai and Chinese dissident Hu Jia had been among the favourites.
Paul Reynolds BBC News, London
The award is certainly unexpected and might be regarded as more of an encouragement for intentions than a reward for achievements.
After all, the president has been in office for a little over eight months and he might hope to serve eight years. His ambition for a world free of nuclear weapons is one that is easier to declare than to achieve and a climate control agreement has yet to be reached.
Indeed, the citation indicates that it is President Obama's world view that attracted the Nobel committee - that diplomacy should be founded "on the basis of values and attitudes that are shared by the majority of the world's population".
Instead the committee chose Mr Obama, who was inaugurated less than two weeks before the 1 February nomination deadline.
While there was support for the decision, notably from world leaders, many others expressed scepticism.
In the US the chairman of the Republican National Committee, Michael Steele, asked a simple question: "What has President Obama actually accomplished?"
Attributing Mr Obama's win to his "star power", Mr Steele said it was "unfortunate" he "outshined tireless advocates who have made real achievements working towards peace and human rights".
Iran's foreign minister said the decision to give the award was taken too "hastily".
"A good timing for the award would be when US troops have pulled out of Afghanistan and Iraq and the United States is standing up for the rights of the Palestinian people," Manouchehr Mottaki told the Mehr news agency.
But he said that if winning the prize encouraged the US president to reject the "warmongering" policies of previous administrations, Iran had no opposition to it.
A large majority of remarks from BBC viewers, listeners and website users also expressed surprise.
Senior Democratic figures rebuffed Mr Steele's remarks, with former Vice-President Al Gore, a joint recipient of the award in 2007, calling Mr Obama's win "extremely well deserved".
Worldwide reaction to Obama winning the Nobel Peace Prize
"I think that much of what he has accomplished already is going to be far more appreciated in the eyes of history," Mr Gore said.
But spokesmen from anti-US Islamist groups such as the Taliban and Hamas focussed on the present, saying they had seen no evidence yet of improvements in security for people in their regions and as such opposed the award.
Since taking office in January, President Obama has pursued an ambitious international agenda including a push for peace in the Middle East and negotiations over Iran's nuclear programme.
Asked why the prize had been awarded to Mr Obama less than a year after he took office, Nobel Committee head Thorbjoern Jagland said: "It was because we would like to support what he is trying to achieve".
He specifically mentioned Mr Obama's work to strengthen international institutions and work towards a world free of nuclear arms. The statement from the Nobel Committee said Mr Obama had "created a new climate in international politics".
THE SELECTION PROCESS
Those qualified to nominate candidates include members of national governments, international judiciary, academics and previous prize winners
Five Norwegians are chosen by Norway's parliament to sit on the Nobel Committee
The committee compiles a shortlist of between five and 20 candidates
The shortlist is considered by the Nobel Institute's permanent advisers, mainly Norwegian academics
The Nobel Committee chooses the winner
Details of the nominations and selection process are kept secret for 50 years
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