As we surmised, Apple waited until just after the end of today's Apple Event to release iOS 9.3. The new version of the mobile operating system was discussed throughout the event, particular the big new features -- Night Shift, new encrypted Notes, and improvements to Health, News, and Apple Music.
To install it, launch the Settings app, then tap General > Software Update. The new operating system will be available for your immediate download and installation.
Enjoy Night Shift -- I've been testing it with one of my devices and I absolutely love having the screen shift to that warmer color at night.