After a private hearing in the Family Division of the High Court in London, the judge ruled that it was in the interests of Jade Bennett, five, and her half-sister, Hannah, three, that the Bramleys be granted temporary custody.
Issuing a court injunction on any further reporting of the family's whereabouts, Mrs Justice Hogg said: "It is important that they [the children] and Mr and Mrs Bramley are given both the time and the freedom that they need to come to terms with what has happened and, in the case of Mr and Mrs Bramley, to plan accordingly."
Mrs Justice Hogg, who made an appeal last November for the Bramleys to return with the two children, said she was "extremely relieved" to hear that they had been found "safe and well".
The Bramleys had gone into hiding with the children after they were told they would not be allowed to adopt them, and had spent four months on the run, evading police with false trails. After making contact with Mrs Bramley's brother, they flew to Stansted airport from the Irish Republic on Saturday and gave themselves up. It emerged they had spent most of the intervening time in a remote corner of the Irish Republic.
Liz Railton, director of Cambridgeshire social services, said her department will continue to oppose the Bramleys' adoption of the two girls.