You can upload the signed APK and make it available on your own website. For Android, it will be sufficient just to host the APK (although you need to do some additional configuration for IIS). For iOS, you can distribute your IPA file using an Over the Air (OTA) manifest. If you choose this option, you still need to register UDIDs and create a corresponding ad hoc provision profile.
From a high-level perspective, this approach looks like this:

You also have to notify your users about a new version being available on your website.