The deliveries are to start in Los Angeles and New York this holiday season and expand to Dallas, Houston, New Orleans, Phoenix and other cities in 2014, The New York Times reported Monday.
"Consumers have shown that there is a market for package deliveries seven days a week, and we are glad to be in a position to partner with Amazon on providing this service," Postmaster General Patrick Donahoe said.
"Now every day can be an Amazon delivery day," said Kelly Cheeseman, a spokeswoman for Amazon.
The USPS lost nearly $16 billion last year and has been struggling to maintain revenue while the Internet contributes to a drop in demand for its services.
The service delivered 69 billion pieces of mail in 2012, down from 92 billion in 2008.
Revenue over the same period dropped from $75 billion to $65 billion. At the same time, shipping packages has grown, reaching 3.5 billion pieces in 2012, the Times said.
The Postal Service said it would seek other partnerships but Amazon would not say if it planned to make similar deals with competitors FedEx or United Parcel Service, which do not deliver on Sundays.
The financial terms of the deal with Amazon were not released, the Times said.