The committee said the EU had helped to transform Europe "from a continent of war to a continent of peace".
The award comes as the EU faces the biggest crisis of its history, with recession and social unrest rocking many of its member states.
The last organisation to be given the award outright was Medecins Sans Frontieres, which won in 1999.
Announcing the award, Nobel committee president Thorbjoern Jagland acknowledged the EU's current financial problems and social unrest.
But he said the committee wanted to concentrate on the body's work over six decades of advancing "peace and reconciliation, democracy and human rights".
Mr Jagland highlighted the EU's work in sealing the reconciliation between France and Germany in the decades after World War II.
It was a unanimous decision by the five-member panel of the Nobel committee, but also came as a surprise to many - not least the pundits who had variously speculated that perhaps the bloggers of the Arab Spring, or a Russian human rights groups might win.
The European Union's achievements are clear, and the Nobel committee has highlighted them. Focusing on a long-term view of the EU's activities the committee spoke of reconciliation following the two World Wars. It mentioned the integration of the Eastern Bloc countries, and the EU's role in delivering stability in the Balkans.
However, they picked a rather strange time to honour the organisation. The eurozone crisis has made the EU look more divided and fragile than it has for decades.
The EU's reconciliation work had now moved to Balkan countries, he said, and pointed out that Croatia was on the verge of membership.
Reacting to the award, EU Commission President Jose Manuel Barroso said on his Twitter feed: "It is a great honour for the whole of the EU, all 500 million citizens, to be awarded the 2012 Nobel Peace prize."
The BBC's Europe correspondent Matthew Price says the EU's achievements are clear, but the committee has picked a strange time to highlight them.
The eurozone crisis has made the EU look more divided and fragile than it has for decades, he says.
The Nobel committee has rarely shied away from controversy with its choice of winner.
US President Barack Obama won the award in 2009, despite leading a country that was fighting two separate wars.
And the choice of detained Chinese dissident Liu Xiaobo in 2010 enraged China, which made an official complaint to Norway.
This year's Nobel Prize for literature winner, Chinese writer Mo Yan, said on Friday he hoped Mr Liu would be freed as soon as possible.