If the previous device has been backed up to your Google account, you will need to download the mobile app onto the new device and select 'Get Account Back' from the welcome screen. This can be done from the prompt when you added your first account to the app or from the settings menu in the app.
After you have restored your new device from your iCloud backup, open the DUO Mobile app on the new device and choose the Reconnect option. For iOS devices, you must have iCloud setup and are backing up your device to iCloud.
If your phone number has not changed, you may be able to use the account restore feature.