The Federal Trade Commission said Apple will make full refunds for any such in-app purchases made by kids using mobile phones and other devices, and incurring charges by accident or without parents' permission.
Apple will have to change its billing practices to make it more obvious that an actual purchase is taking place during the course of the game or app.
The commission said it had received tens of thousands of complaints about unauthorized charges.
Edith Ramirez, the agency's head, said the settlement involves mobile apps and charges racked up when kids bought things such as virtual currency or dragon food. In some cases, Ramirez said, charges ran into the hundreds and even thousands of dollars.
One parent told the FTC that her daughter had spent $2,600 in "Tap Pet Hotel," a game in which kids can build their own pet hotel. The game is free to download and play but involves in-app purchases where kids buy treats and coins for their pets.
Others consumers reported unauthorized purchases by children totalling more than $500 in the apps "Dragon Story" and "Tiny Zoo Friends."
"You cannot charge consumers for purchases they did not authorize," Ramirez said.
According to FTC complaint, when parents entered their password while a child played a game, Apple did not make it clear that that they unwittingly may be buying something in the game the child had clicked on, such as a chest of gems or treats for a virtual pet.
Parents also were not told, the FTC said, that entering their password opened a 15-minute window in which kids could make unlimited purchases without any further action by an adult.
Apple will have until Mar. 31 to come up with a billing system that ensures the company obtains consumers' informed consent before billing them for in-app purchases.
The $32.5 million payout is a minimum. As part of the settlement, Apple must pay full refunds to consumers for kids' unauthorized purchases, so that figure could climb. If it doesn't rise to $32.5 million, the difference would be paid to the FTC, Ramirez said.
Apple is the world's most valued company as measured by market capitalization.