Upgrade iOS 10 beta to iOS 10 final/public release
You can just do a normal software update from Settings > General > Software Update.  The release version will overwrite the beta version. See Apple's Beta software FAQ's* (https://beta.apple.com/sp/betaprogram/faq):


  To get a shipping release of iOS on your iPhone, iPad, or iPod touch, you can simply install the final version of the software you are testing when it appears in Software Update. 


Apple's technical note about iOS beta software* (https://support.apple.com/en-us/HT203282) documents the process for upgrading from the beta to final release of iOS:


  Download the final version of iOS
  
  If you have an iOS beta version and want to download the final version, follow these steps:
  
  
  Connect your device to iTunes.
  While your device is connected, force it to restart. Press and hold the Sleep/Wake and Home buttons at the same time. Don't release when you see the Apple logo. Keep holding until you see the Recovery Mode screen.
  When asked, choose Update to download and install the latest non-beta version of iOS.
  
  
  An update install won't affect your content or settings.


*URLs left intentionally, do not edit to remove.