The scheme, drawn up in coordination with the UN refugee agency (UNHCR), is aimed at children deemed at risk of child labour, forced marriage and other forms of abuse or exploitation.
It will affect children on their own and those accompanied by relatives or carers, and will see several hundred people resettled in the coming year, the Home Office interior ministry announced.
The commitment is in addition to Britain's pledge to resettle 20,000 of the most vulnerable refugees from camps on Syria's borders by 2020. So far, more than a thousand - half of them children - have arrived.
"We have always been clear that the vast majority of vulnerable children are better off remaining in host countries in the region so they can be reunited with surviving family members," said Home Office minister James Brokenshire.
More From This Section
"However, there are exceptional circumstances in which it is in a child's best interests to be resettled in the UK."
The UNHCR's representative to Britain, Gonzalo Vargas Llosa, said the new scheme was an "important contribution" to the agency's efforts to address the needs of refugee children.
The British government also announced it would be offering 75 expert personnel to help with the processing and administration of migrants in reception areas in Greece, as part of an EU deal with Turkey.