Dennes Torres shows off what the Azure Resource Mover can do:
If you include the need to copy a resource or set of resources, instead of only moving, the list expands a lot.
Azure already offers the resources to do this: ARM templates, automated deployments, Data Sync, Recovery Services Vault, VM replication and so on. The problem is that sometimes, to move a set of objects together, you may need to use many of these services and understand how to use them.
The solution is a new free service, still in preview, called Azure Resource Mover. This service reduces the complexity of moving resources, minimizing the number of decisions needed on how the resources will be moved. More than that, the last step, deleting the source of the move, is optional, as you will see in detail later. You can use this feature, not only to move resources, but also to copy and distribute them across many regions. During the move process, only one side (source or destination) will be active, but once you finish the move, if you decide not to delete the source, you have in fact a new deployment of the solution.
This is a fairly detailed tutorial, so check it out.