On Android devices, install the application on your new device and transfer your account data from your old device using the account migration service, accessible from Settings / Help / Accounts / Account migration.
On iOS devices, you should be able to use the standard iOS back-up/restore services, with the encryption option “ON”.
Account migration between iOS and Android devices, as well as back-up/restore on external media to cope with lost or stolen devices, are currently under development.