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Some of the "most vulnerable" Syrian refugees will be temporarily resettled in the UK, Deputy PM Nick Clegg says.
He said girls and women who had been victims of or were at risk of sexual violence, torture victims, and elderly and disabled people would get priority.
This meant the coalition was ensuring Britain's "long and proud tradition of providing refuge" lived on, he said.
The government expects the number of refugees accepted to be in the hundreds but has not set a specific target.
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AnalysisJames LandaleDeputy political editor
The government has been reluctant to admit any Syrian refugees to the UK, preferring to focus its humanitarian aid on refugees in the region.
But a fear of looking hard hearted and the threat of parliamentary defeat on Wednesday changed minds in Downing Street.
The deputy prime minister Nick Clegg said Britain had a moral responsibility to help and several hundred refugees would now be able to come.
It is not clear where the refugees will go or how long they will stay but it is expected they will get temporary visas that will be reviewed after three years.
The government is still refusing to take part in a resettlement scheme run by the UN high commissioner for refugees.
But the agency welcomed the government's offer and said it would help officials identify the most vulnerable people.
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The UK's resettlement programme is to be separate from the ongoing UN High Commissioner for Refugees scheme which has seen Germany commit to admitting more than 10,000 Syrian refugees and France take 500.
Home Secretary Theresa May is expected to spell out more details of the government's plan to MPs later.
During exchanges in the Commons on Monday, the government faced criticism from MPs of all political parties for declining to participate in the UN-led scheme.
The deputy prime minister's announcement pre-empted a Labour-led debate on the issue, where the government was facing the prospect of a Commons defeat over its refusal to sign up to the UNHCR initiative.
Mr Clegg said: "The coalition government wants to play our part in helping to alleviate the immense suffering in Syria. The £600m we have provided makes us the second largest bilateral donor of humanitarian aid in the world.
"But as the conflict continues to force millions of Syrians from their homes, we need to make sure we are doing everything we can.
"We are one of the most open-hearted countries in the world and I believe we have a moral responsibility to help.
The UK says half of Syria's nine million population have been displaced
"The UN High Commission for Refugees - which backs our new resettlement programme - has said the highest priority should go to women and girls who have experienced or are at risk of sexual violence; the elderly; survivors of torture and individuals with disabilities, so that's who we'll target.
"Sadly we cannot provide safety for everyone who needs it, but we can reach out to some of those who need it most."
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WHERE REFUGEES ARE GOING?
US: No limit set
Source: UNCHR (20 January)
The BBC understands the refugees will be given temporary visas allowing them to stay for at least three years.
The visas will then be reviewed on a case-by-case basis taking into account personal circumstances and the situation in Syria.
Mr Clegg added: "They will be here for a certain period of time and what we of course want and I suspect they will want as well… is to return eventually to Syria, when as I think everybody hopes normality finally is restored to the country."
The UNHCR said it would help the UK identify the most vulnerable people.
Its UK representative, Roland Schilling, said the UK move was "an encouraging and important step, reaffirming the UK's commitment and contribution to international relief efforts".
Shadow Home Secretary Yvette Cooper: ''It is a good thing that the government has completely reversed its position''
Shadow home secretary Yvette Cooper said the government's move was a "big reversal" but that "compassion and common sense have won through".
"Vulnerable Syrian refugees, torture victims, abandoned children and those struggling to cope or survive in the camps desperately need sanctuary and Britain has a moral obligation to help," she said.
But she said the UK should be working with the UN to decide on numbers rather than setting up a "parallel programme" of its own.
Refugees fleeing Syria
The move was welcomed by MPs from all sides of the Commons, former Lib Dem leader Sir Menzies Campbell saying it gave the UK flexibility to help those whose suffering had been the most "grievous".
But Conservative Brooks Newmark - an expert on Syria - said numbers should be limited and those countries not making such a big contribution to the aid effort should be taking in more refugees than the UK.
UKIP leader Nigel Farage also backed the move, saying a clear distinction must be made between genuine refugees from persecution and economic migrants.
The Refugee Council's Maurice Wren said the move had been a "long time coming" but the UK was standing up for an important principle.
And Amnesty International UK director Kate Allen said: "This move is long overdue but of course it's never too late to do the right thing."