I recently upgraded from Galaxy S6 Edge to new Galaxy S7 Edge and like OP I didn't want to lose my old Viber conversations. I successfully transferred all the Viber messages along with the photos, videos, and other attachments from my old Android device (S6 edge) to new Android device (S7 edge) with the the help of a paid third-party software called Android Viber Transfer mentioned in this guide.
It costs $19 but I guess it’s the only tool to transfer Viber messages from one phone to another (Android to Android and iPhone to iPhone) because on Google I found 3-4 websites that are talking about this tool. Free version lets you transfer only 20 messages which is kind of useless. These are the steps that need to be followed in order to transfer Viber messages from one Android device to another:
Launch the app on your computer and connect your old Android device
with to your computer via USB cable. Make sure USB debugging is
enabled on your device.
Tap ‘Back up my data’ on your Android and you’ll be able to see all
your Viber chat history on the UI of this program.
Right click on your Android and choose “Backup Messages” to
backup your Viber messages to the local database on your computer.
Move the SIM card to your new Android device, download the Viber
app on your device and verify your phone number.
Finally, connect your new Android device to your computer, right
click on the database that you’ve created and choose “Restore
I tried this on my non-rooted S7 edge running Android 6.0.1 Marshmallow and it worked for me. I hope my answer will help the folks those who are looking to transfer Viber messages from their old device to new device as currently there isn’t native/official solution for this.