DNA tests are to be ordered in a bid to end lengthy court battles over a child's parentage.
From September, all family court judges in England will be able to order the tests.
Justice Minister Simon Hughes said the decision would speed up court cases.
He told the BBC: "I am determined that all cases involving children should be resolved quickly and wherever possible outside court.
"However when they do come to court they should be resolved in a civilised way so that children don't suffer.
"Unambiguous and conclusive DNA tests will prove parentage and help to end acrimonious and embarrassing court battles."
Funding for the over of between £500,000 and £1 million a year will come from the budget of the Children and Family Court Advisory and Support Service (Cafcass).
The Ministry of Justice said funding for DNA testing in private family law cases followed the introduction last year of the biggest reforms to the family justice system for a generation.
These have placed children at the heart of every case and have cut to 29 weeks the time which care cases are taking.
Reforms have included the introduction of the new Family Court in England and Wales with a simpler system and compulsory family mediation information meetings so separating couples must consider alternatives to harmful and stressful court battles when they are resolving financial matters and arrangements for child contact.
Liz Cowell, family lawyer at Slater and Gordon, said: "This will assist in those cases where mothers try to allege that the father has no right to contact because he is not the natural parent.
"The change will also assist in cases where paying parents try to dodge supporting their children with claims that they are not the biological father.
"We have experienced situations where we act for a mother and the father says he wants contact with his child, but he will not pay maintenance as he is not the father."
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