Once a month, members can download a book for free from the library, which boasts more than 145,000 books.
Rowling only recently permitted e-books of the Potter series and has been offering them through her own website, Pottermore.com. The e-books on the Kindle will be available in English, French, Italian, German and Spanish.
Financial terms were not disclosed for Amazon.com's "licensing agreement" with Rowling.
The Associated Press contributed to this report.