Apple announced the Files app as part of iOS 11 on stage at WWDC 2017, saying that, in addition to on-device documents and iCloud Drive, third-party file storage apps will be able to integrate with Files. Now, one of those partners, Dropbox, has confirmed that it will indeed offer support for Files in iOS 11.
From Dropbox:
More than that, though, it will extend file capabilities system-wide. You’ll be able to access files in your Dropbox account from third-party apps just as if they were stored on your iPhone or iPad. This integration will even work with Dropbox-specific features for teams, like commenting and viewer info, letting you collaborate on files from any app that supports file browsing.
File.app gives you a central location for all of your file storage in iOS 11, no matter if you keep items in iCloud or in some other service. It also syncs over the file tags you’ve created in macOS, offering a seamless file experience between Apple’s mobile and desktop operating systems.