The accord includes a recognition to limit temperature rises to less than 2C and promises to deliver $30bn (£18.5bn) of aid for developing nations over the next three years.
It outlines a goal of providing $100bn a year by 2020 to help poor countries cope with the impacts of climate change.
The agreement also includes a method for verifying industrialised nations' reduction of emissions. The US had insisted that China dropped its resistance to this measure.
But the BBC's environment correspondent Richard Black says the Copenhagen Accord looks unlikely to contain temperature rises to within the 2C (3.6F) threshold that UN scientists say is needed to avert serious climate change.
US President Barack Obama described negotiations as "extremely difficult and complex", but said they had laid "the foundation for international action in the years to come".
"This progress did not come easily, and we know that progress on this particular aspect of climate change negotiations is not enough," he added.
Several South American countries, such as Nicaragua and Venezuela, were among a group saying the agreement had not been reached through proper process.
AT THE SCENE
Richard Black, BBC News environment correspondent
Ministers and scientists and campaigners who dedicated huge swathes of the last year to making a tough deal happen watched aghast as Chinese and US leaders and their entourages flew in, took over the agenda and emerged with what was basically their own private deal, with leaders announcing it live on television before others realised it had happened.
As you'd expect, leaders from EU countries and the developing world that really don't like this deal have been assuming rictus grins and telling us it's a "good first step".
Problem is, Bali in 2007 was the "first step"; come to that, Rio in 1992 was the "first step". Where we go from here isn't clear at the moment.
Environmental campaigners and aid agencies branded the deal toothless and a failure.
Robert Bailey, of
, said: "It is too late to save the summit, but it's not too late to save the planet and its people."
Mr Ban told journalists: "It may not be everything we hoped for, but this decision of the Conference of Parties is an essential beginning."
The Copenhagen Accord is based on a proposal tabled on Friday by a US-led group of five nations - including China, India, Brazil and South Africa.
The UK's Climate Change Secretary Ed Miliband said it was very important that the adoption of the accord would allow the flow of money to begin.
But, he said: "We recognise there could have been more ambition in parts of this agreement. Therefore we have got to drive forward as hard as we can towards both a legally binding treaty and that ambition."
backed the deal and his statement was denounced by other delegations.
In a further twist, says BBC environment reporter Matt McGrath, there is to be a list of those countries in favour and against on the front of the final document, with some experts suggesting money will only flow to those who say yes.
During the summit, small island nations and vulnerable coastal countries had demanded a binding deal to limit emissions to a level preventing temperatures rises above 1.5C (2.7F) over pre-industrial levels.
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