If you're transferring between iOS and Android, and have a current subscription, you can  share your current subscription to the new device. Your subscription will continue to be billed through the app store that it was purchased through (Google Play for Android, App Store for Apple).

If your new device is a Windows Phone, Windows 8, or a Mac, there is currently no way to transfer your subscription or purchases.

iOS and Android Devices
If you're not changing platforms, using the Apple/Google account that was used to originally purchase the subscription, you can easily  restore the subscription to your new device.

Other Devices
Instructions for downloading previously purchased apps can be found here:

• Mac
• Windows Phone