For $100 a year, Amazon’s Prime subscription gets you unlimited two-day shipping on Amazon.com, and access to the retailer’s library of streaming movies, TV shows and music. Now, it’ll get you unlimited photo storage, too. On Tuesday, Amazon added a feature called Prime Photos into the mix, letting Prime subscribers upload as many photos as they’d like to Amazon’s Cloud Drive storage service.

Those who do buy into Prime will be able to upload their photos using the Amazon Cloud Drive Photos apps on Android or iOS, as well...