AzCopy Preview (v10) now supports Amazon Web Services (AWS) S3 as a data source and can copy an entire AWS S3 bucket (or even multiple buckets) to Azure Blob storage.
To copy an S3 bucket to a Blob container, use the following command:
azcopy cp "https://s3.amazonaws.com/mybucket/" "https://mystorageaccount.blob.core.windows.net/mycontainer?" --recursive
To get started, read the documentation here.
Give us feedback
AWS S3 as a source in AzCopy is currently in preview. Try it, and give us your feedback by posting on our source code repository on GitHub!