A High Court judge yesterday granted the runaway couple Jeffrey and Jennifer Bramley temporary custody of their foster daughters, Jade and Hannah Bennett.
Sitting in London, Mrs Justice Hogg ruled it was in the best interests of the two girls for them to remain with their foster parents for the time being.
It is understood the family will remain for at least another week at the secret address where they have been staying since their return on Saturday after four months on the run.
After the hearing, Cambridgeshire County Council said it was pleased with the co-operation its staff had received from the Bramleys since they gave themselves up.
However, the Council made it clear it would still oppose attempts by the couple to adopt Jade (5) and Hannah (3).
At the High Court Mrs Justice Hogg said she was "extremely relieved" that the two girls had been found safe and well.
The judge paid tribute to the police, public and the media for their efforts in searching for the missing family.
Mrs Justice Hogg made the two girls wards of court and said their future would now be decided by the High Court, with the Official Solicitor acting on their behalf.
She also imposed an order banning the reporting of any further information about the case which had not already been made public.
The judge said: "Now that Jade and Hannah have been found, it is important that they 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 for the future accordingly.
There was no comment after the brief open court hearing from lawyers representing the Bramleys.
Mr Paul Duckett, the natural father of Jade, said he would accept Mrs Justice Hogg's decision but would be taking immediate steps to try to obtain a visit with his daughter.