London will allow refugees living on a UK military base in Cyprus since 1998 to settle in Britain following a long legal dispute, a spokesman said on Tuesday.
The group of six families are among 75 people from Ethiopia, Iraq, Sudan and Syria who landed on the southwest coast of Cyprus after the boat in which they were travelling to Italy foundered.
They were recognised as refugees but then interior minister Theresa May decided they could not be admitted to Britain and they have since been pursuing a legal challenge.
The refugees have been living on the Dhekelia base, which is British sovereign territory.
"Given the unique and highly unusual circumstances of these refugees and their children we have made an exceptional decision to bring an end to this long-standing issue, enabling them to leave Dhekelia immediately and settle in the UK," a British interior ministry spokesman said.
While they could in theory claim asylum in Cyprus, many say they have little prospect of finding work or permanent residency on the island.
The dispute has rumbled on for so long that many of the refugees have married and had children, all within the boundaries of the seven-square-kilometre (three-square-mile) outpost where they live, although they are able to go outside.
"We are delighted that the current Home Secretary has done the humane thing and agreed to grant our clients and their families leave to enter the UK for permanent residency," Tessa Gregory, a solicitor at Leigh Day, said in a statement.
Tag Bashir, the lead claimant, said: "We only want to thank everyone who has worked so hard to help us escape this 20-year nightmare.
"I cannot express how happy our families are to be given the opportunity to come to the UK and start our lives again," he said.