Mr Alan and Mrs Judith Kilshaw yesterday lost their legal battle to keep the nine-month-old babies they said they had legally adopted over the Internet.
Mr Justice Kirkwood made an order in the High Court in London which will result in the twins being returned to Missouri in the US, where they were born.
In a statement issued later the judge said Belinda and Kimberley would be looked after by foster parents in the US pending a decision by a Missouri court as to what was in their best interests.
The statement read: "The court held that it would not be in the welfare interests of the twins for them to be returned to Mr and Mrs Kilshaw."
The couple, from Buckley, north Wales, who say they paid a US baby-broker £8,200 to adopt the girls, began a legal battle with Flintshire Social Services in January when it took the girls into care.
Mr and Mrs Kilshaw left the court via a private judges' entrance without commenting, but their lawyers announced from the front of the Royal Courts of Justice in the Strand that the couple were "very disappointed with the decision".
They said they only wanted the best for the twins and were considering taking the case to the Court of Appeal.
Belinda and Kimberley, also the subject of a custody battle involving their natural mother and father, are currently being cared for by foster parents in north Wales.
Today's private hearing in Court 43 in the Family Division was punctuated by outbursts from Mrs Kilshaw, who emerged from the courtroom flanked by High Court officials, screaming at gathered media representatives.
Mrs Kilshaw (47) yelled: "There is no justice. They said I lied."
As she struggled with the official, she said: "You want everything, don't you? My life and my kids."
Twenty minutes later she was again taken from the court, screaming abuse, and was led away by an official and her daughter, Kaley (18).