The four took their legal fight before the European Court of Human Rights, arguing they had not been informed that their abuser had criminal convictions.
The ruling found social workers were negligent in the care of the victims, the first time social workers have been found liable.
The decision could open the floodgates for compensation claims against social workers in cases where children are not adequately protected from a potential abuser.
The victory follows 13 years of campaigning by the family and their legal representatives who had exhausted all options in the British courts.
The family claimed their human rights were breached after social workers in Dumfries failed to tell them of criminal convictions against their stepfather, who had been abusing them physically and sexually.
Abuse victim Lesley Robertson said: "Mental, physical, sexual abuse, he pitted us all against each other.
"Every day was a nightmare with him."
Vindicated
William Haining was convicted twice, in 1977 and 1989, for abusing the youngsters, who were as young as seven at the time.
At his second trial at Dumfries Sheriff Court, it emerged social workers had been aware of his first conviction but had allowed Haining to continue living with the family.
But in another case in 1996 the House of Lords ruled social workers could not be sued for negligence where they were involved in discretionary child protection measures.
The family's solicitor Lyall Moodie said the family had been vindicated by the European court.
He said: "The significance of this case is that social workers are no longer above the law and not immune to being sued for negligence.
"They didn't protect those girls.
"They completely failed in their duties for these young girls who were very vulnerable in the situation."
The victims have been awarded damages of between £10,000 and £20,000.
However, they said the legal princilpe was more important than what they described as "blood money".
Dumfries and Galloway Council said the implications of the judgement against its predecessors were being studied.
Chief social work officer Keith Makin said: "The system has been completely overhauled and many more safeguards are in place to protect children in circumstances such as these."