It is to give back 32.5 million dollars (£20 million) settle a federal case involving the purchases.
The Federal Trade Commission said Apple will make full refunds for any such in-app purchases made by youngsters while playing on mobile phones and tablets - and incurring charges without parents' knowledge or permission.
The commission said it had received tens of thousands of complaints about unauthorised charges.
Its head, Edith Ramirez, said the settlement only involved children's mobile apps and charges racked up when they bought things such as virtual currency or dragon food.
In some cases charges ran into the hundreds and even thousands of dollars.
The FTC said the apps included a 15-minute window in which passwords were not needed to make the purchases, but that Apple did not tell users that.
Apple is the world's most valued company as measured by market capitalisation.