Hi,
Could you please suggest back up approach to backup tape data and data in disks from on-premises to Azure?
It depends what backup solution you're using today, many offer an integration to Azure which makes the transition easier.
Move your long-term storage from tape to the Azure cloud
https://learn.microsoft.com/en-us/azure/backup/backup-azure-backup-cloud-as-tape
What storage tiers are appropriate and what are the recovery mechanisms?
This depends on your organisation's requirements and needs, you can have a look here for the different tiers options:
https://learn.microsoft.com/en-us/azure/storage/blobs/storage-blob-storage-tiers?tabs=azure-portal
Also, if the data is required to be available at on-premises only, what is the recovery approach to recover data on tape drives and disks at on-premises to Azure?
If your data is required to be available at on-premises you cannot back it up to any cloud, then you will have to continue using your tape drives or local disk storage.
Best regards,
Leon