Several hundred will be resettled over the next year with a view to resettling up to 3000 over the next three years.
The scheme will not solely target unaccompanied children but extend to vulnerable 'children at risk', such as those threatened with child labour, child marriage and other forms of abuse or exploitation.
The new programme, said to be the largest resettlement effort aimed specifically at children at risk from the region, is in addition to the UK government's commitment to resettle 20,000 Syrian refugees under the Vulnerable Persons Resettlement Scheme (VPRS).
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The VPRS has already resettled over 1000 Syrian refugees, over half of them children.
Britain has been working closely on the migrant crisis engulfing much of Europe with the United Nations High Commissioner for Refugees (UNHCR).
Reaction to the announcement, on Thursday, came from UK immigration minister James Brokenshire, who said, "The UK is committed to providing life-saving support and assistance to the vulnerable children who have been unjustly impacted by this ongoing humanitarian crisis.
"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. However, there are exceptional circumstances in which it is in a child's best interests to be resettled in the UK.
"We have engaged with a number of NGOs, including the UNHCR on the best way to provide protection to refugee children and ensure their welfare and safety remain at the heart of every decision made."
He added, "This new scheme compliments our ongoing work within Europe to assist vulnerable migrant children. This includes the £10m Refugee Children Fund to identify and support vulnerable children and strengthen child protection and family reunification systems."
Further comment came from the UNHCR representative to the UK, Gonzalo Vargas Llosa, who said, "The launch of the UK's resettlement scheme for refugee children at risk is an important contribution to UNHCR's continuing efforts to address the global protection needs of refugee children, including through resettlement and other pathways for admission.
"We welcome the scheme's focus on children at risk, including unaccompanied and separated children, and the UK's commitment to upholding the principles of child protection and the child's best interest, in implementing the programme."
The UK has also outlined further details of its contribution to the EU-Turkey migration agreement, which aims to prevent illegal crossings from Turkey to Greece.
Britain says it will offer 75 expert personnel to help with processing and administration of migrants in reception centres.
A UK diplomatic source said, "This will help to ensure that vulnerable people, including children, are identified and can access asylum systems as quickly as possible, while other migrants will be returned to Turkey in accordance with the EU-Turkey deal."
The new agreement is in addition to the work being undertaken by Kevin Hyland, anti-slavery commissioner, to visit hotspots and assess what more can be done to ensure unaccompanied children are protected from child traffickers.