The initial claim by Rowling and her husband was thrown out by a London court last year, prompting the couple to appeal.
In a written judgment on Wednesday, a panel of judges upheld the appeal, a ruling which Rowling and husband Neil Murray welcomed.
"We understand and accept that with the success of Harry Potter there will be a measure of legitimate media and public interest in Jo's (Rowling's) professional activities and appearances," the couple said in a statement.
"However, we have striven to give our children a normal family life outside the media spotlight.
"We are immensely grateful to the court for giving our children protection from covert, unauthorised photography; this ruling will make an immediate and material difference to their lives."
Anthony Clarke, one of the judges hearing the appeal, said the child of a famous parent should have the same rights as that of "ordinary" parents.
"If a child of parents who are not in the public eye could reasonably expect not to have photographs
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