Up to 40 new areas will benefit from the programme, Supporting Families; Investing in Practice, which offers innovative approaches to helping families affected by issues such as domestic violence, substance misuse, or addiction, to stay together.
It has been modelled on existing Family Drug and Alcohol Courts (FDACs), which provide a problem-solving approach to care proceedings, as well as the Family Group Conferencing programme, an initiative that works with whole families with children at immediate risk of being taken into care.
Isabelle Trowler, chief social worker for children and families, said the funding is an "important milestone" in the work that had been done to support vulnerable families.
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Trowler said that when the Children's Social Care Innovation programme was launched four years ago, the government "held high hopes for identifying promising practice which we could spread across England".
"Extending the reach of these tested programmes is indicative of the relentless hard work of everyone involved in developing practice to help support children and families," she added.
The programme will be rolled out in partnership with the What Works Centre, which will oversee the implementation of the additional support in 40 council areas.
The centre will collect evidence of the programme's effectiveness in helping vulnerable families to work through their issues and stay together where it is in the best interests of the child.
The government said it was part of a wider drive to improve outcomes for children in need of support from a social worker.
Children's minister Nadhim Zahawi said rising numbers of children were being taken into care from families where parents were struggling with their own issues.
"Every child, no matter what hand they have been dealt, deserves the opportunity to grow up in a stable, loving family so they can develop into confident adults equipped to take on life's challenges successfully.
"Projects like these are making sure vulnerable families get the support they need from experts who can help them address their problems head on and stop them from spiralling out of control," he said.
Steve Bambrough, a member of the FDAC National Partnership, said problem-solving models such as offered by FDACs, achieved better outcomes for parents, children and are cost effective.
"It is a fair and trauma-informed approach which gives people the best chance of change and that's why it makes for better justice," he said, adding: "We're delighted that this funding will enable more families and local authorities to have access to a compassionate and evidence-based approach to family justice."
The £15m funding follows £84m announced by the Department for Education last month to help up to 20 councils support families to stay together through the Strengthening Families, Protecting Children programme.
These projects aim to build resilience among more vulnerable families and improve how councils design and run services.