"There is no specific minimum age necessary for the child," the judges wrote in their decision, adding that parents could request the details on behalf of their children.
The judges did attach conditions, notably that parents must be able to prove that the child has requested the information, and said that possible effects on the private life of the donor must be taken into account.
But they also found that the right of the child to know had "generally a greater weight" than the father's right to be undisturbed.
A pair of sisters, aged 12 and 17, who were both fathered from donor sperm, brought the case to the supreme court after disputing the current rule that a donor's identity can only be revealed when the child or children in question have reached the age of 16.
At the time of conception, the parents of the young plaintiffs waived their right to know who the donor was.
The law in Germany previous to the Supreme Court's decision was patchy and the BGH hopes that Wednesday's decision has clarified where the law stands.
In 1989, the courts decided that every person had the right to know their roots and who or where they came from. In 2013, the first courts agreed that sperm donors could be identified if their offspring asked to do so.
In 2007, laws stated that fertility clinics had to have permission from their donors to disclose their identity or not in the future. Disclosure forms and donor records also have to be kept on hand for 30 years, according the the state ruling.
The clinics have always preferred to be able to promise anonymity.
Prior to Wednesday's hearing, the lawyer of the plaintiffs had spoken out in favour of the right to know.
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"The rights of the children should carry more weight than the rights of the sperm donors," he said.
BGH justice Hans Joachim Dose had previously said that the rights of children did indeed carry weight, but it was also a decision as to the rights of anonymity and to whom the clincs have obligations – their donors or the happy results of their transactions.
The numbers of people currently alive in Germany who were fathered by sperm donations is estimated to be around 100,000. Another 1,500 to 5,000 children are conceived annually using donor sperm.