Blizzard has updated its Battle.net mobile app. For a few hours, the Authenticator has indeed been an integral part of the app, which allows you to do without the application specially dedicated to authenticating your account.
Once the Battle.net app is updated, you can go through the validation process. It will take you regarding thirty seconds. To activate the Authenticator in the BN mobile application, you will also need to use the Authenticator app. Once setup is complete, you can uninstall the old Authenticator app.
Note that as of this writing, the update is exclusively available on iOS devices, namely Apple’s iPhone and iPad. No doubt the update will arrive shortly on the Android side. Thanks to Benoit for the info.