[Update:  2018-10-19] The Background Geolocation plugin version 2.14.0+ for Ionic now provides its own Typescript API!  Read about it here.

Yes, the cordova-background-geolocation plugin works fine with Ionic 2.  I really don't see a great need for a definitions file.  The Demo App is now built with Ionic 2.

Here's a simple Ionic 2 implementation: