Mr Obama claimed that the deal, salvaged from the wreckage of failed negotiations, would allow nations to move towards a legally binding deal next summer in Mexico.
Critics immediately condemned the declaration, which was made after a second meeting between Mr Obama and Chinese premier Wen Jiabao, as completely meaningless.
The watered-down declaration that was being worked on last night commits countries only to aim for targets to cut harmful emissions and provide information for international analysis.
The draft text for the declaration fell far short of the ambitions environmentalists and many politicians, including Gordon Brown, had for the conference.
However, there was some success for Mr Brown as a deal providing £60bn a year to fight climate change, championed by the Prime Minister, was also on the way to being agreed, along with a 2ºC limit on global temperature rises.
“No country is entirely satisfied with each element but this a meaningful and historic step forward and a foundation from which to make further progress,” said a senior US official.
President Obama admitted the deal was “not sufficient” to reach the 2050 goals, but as he left Copenhagen before the final text was issued he said it was a “historic” and meaningful agreement.
Responding to the details emerging from the Copenhagen conference centre, Greenpeace UK executive director John Sauven expressed disappointment.
“It seems there are too few politicians in this world capable of looking beyond the horizon of their own narrow self-interest, let alone caring much for the millions of people who are facing down the threat of climate change,” he said.
“It is now evident that beating global warming will require a radically different model of politics than the one on display here in Copenhagen.”
The absence of any new concessions in Mr Obama’s speech and his attempt to hector China into concessions cast a shadow over the last day’s negotiations
The talks reached an impasse as China, now the world’s biggest polluter, firmly resisted proposals for the international verification of carbon cutting measures after claiming to have been “humiliated” by Barack Obama’s speech.
It took a second meeting with the Chinese for Mr Obama to secure a deal.
As the arguments over the final text continued late into the night, the UK delegation said it was confident agreement would be reached on limiting global temperature rises to 2ºC.
“There has been real movement this evening and we’re more hopeful a deal can be done tonight,” said a British official close to the talks.
“Final details are still being nailed down but we are now confident that we can get the two degrees target agreed.”
Poorer island nations, who are already feeling the effects of global warming lapping on their shorelines, wanted temperature rises limited to 1.5ºC and a two-degree deal was always on the cards.
Gordon Brown, who spent four days in intense negotiations in Copenhagen, took away some succour in having his plan for a £60bn climate change fund agreed.
The Prime Minster basked in the admiration of other nations who gave him credit for his efforts in bringing agreement closer.
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