Handling image (or other binary object) uploads via Web API for storing in Azure blob storage without using the local file system (handy if, for example, you’re using Azure Websites) seems to be a frequently asked question.
I’ve not tested this in anger yet but I’ve posted my own attempt at solving this issue as a gist on GitHub and shown below. It seems to work but as I say I’ve not tested it in anger, only in fairly limited scenarios.
If you use my Azure Application Framework I’ve also added a GetMultipartStreamProvider method to the IAsynchronousBlockBlobRepository interface that provides a pre-configured implementation for a given blob container.
Hope thats helpful.