The company also promised to change its billing practices for so-called in-app purchases "to ensure that it obtains express, informed consent from consumers before charging them for items sold in mobile apps," the Federal Trade Commission said Thursday.
The unauthorized charges began in 2011 for virtual items purchased on apps sold by Google Play for use on Android mobile devices, the agency said. Some parents complained their children racked up hundreds of dollars in charges that never were authorized.
"As more Americans embrace mobile technology, it's vital to remind companies that time-tested consumer protections still apply, including that consumers should not be charged for purchases they did not authorize," said Edith Ramirez, the agency's chairwoman.
Google agreed to send out a minimum of $19 million in full refunds for charges incurred by app users who were less than 18 years old.
The agency has been cracking down on unauthorized in-app purchases by children of virtual items for use in games and other apps. The items can cost anywhere from 99 cents to as much as $200.
In January, Apple Inc. agreed to pay at least $32.5 million in refunds to consumers for such purchases.
And in July, the agency filed a complaint against Amazon.com, alleging it unlawfully billed parents millions of dollars for unauthorized purchases through apps on the company's Kindle Fire and other mobile devices.
In mid- to late-2012, Google began asking for the account holder's password in a pop-up box before billing for an in-app purchase. But the box contained no information about the charge and once the password was entered, children could make unlimited purchases for the next 30 minutes, the FTC complaint said.