You may already know that you can use Azure Data Box to migrate on-premises workloads to Azure (from backups to remote/branch office data).

If you need to know more about Azure Data Box you can go there

This offer has been in preview for the past few month and is now in GA (General Availability).

In addition, Azure Data Box is going to support Azure Blob Storage (preview), allowing you to copy your data to a Blog Storage using the REST API.

You can get all the current requirements to use Azure Data Box with Azure Blob Storage here and then you can follow this tutorial to start using it