Apple will refund customers at least $32.5m (£19.9m) after a settlement with the US Federal Trade Commission (FTC).
The refund agreement settles long-standing complaints over in-app purchases made by children without their parents' consent.
Apple will also be required to change its billing procedures to make sure customers have given consent before they are charged for in-app purchases.
The company said it had settled rather than take on a "long legal fight".
"This settlement is a victory for consumers harmed by Apple's unfair billing, and a signal to the business community: whether you're doing business in the mobile arena or the mall down the street, fundamental consumer protections apply," said FTC Chairwoman Edith Ramirez in a statement.
"You cannot charge consumers for purchases they did not authorize."
'Tens of thousands'
The FTC's complaint alleged that Apple failed to inform parents that by entering a password they were approving a single in-app purchase and also 15 minutes of additional unlimited purchases their children could make without further consent.
It also said that Apple often presented a password prompt screen for parents to enter their details without explaining that this would finalise any purchase made in the app.
The FTC also noted that Apple received at "least tens of thousands of complaints" about unauthorised in-app purchases by children.
One woman said her daughter had spent $2600 in one app.
This refund settlement only covers customers who have made purchases through Apple's US app store but the BBC's technology editor Rory Cellan-Jones says Apple has previously almost always refunded parents in the UK who have complained about big bills from their children's in-app purchases.
The changes to Apple's billing process, which means express consent must be obtained before in-app charges are made, must be in place by 31 March, said the FTC.
In an internal email obtained by the website 9to5Mac, chief executive Tim Cook told Apple employees that the FTC's proposals were in line with the company's own intentions.
"The consent decree the FTC proposed does not require us to do anything we weren't already going to do, so we decided to accept it rather that take on a long and distracting legal fight," he said.
He also explained that Apple began setting out a process to refund customers last year.
"We wanted to reach every customer who might have been affected, so we sent emails to 28 million App Store customers - anyone who had made an in-app purchase in a game designed for kids.
"When some emails bounced, we mailed the parents postcards.
"In all, we received 37,000 claims and we will be reimbursing each one as promised."
Apple's App Store offers many games for children, a large number of which allow in-app purchases to be made. These purchases can include virtual items or currency, and typically allow faster progression in the game.
In-app purchases can range in cost - from 99 cents to just under $100.