Automattic, the company that maintains WordPress, also maintains a widely used plugin called Jetpack. Within Jetpack, there is a feature called Photon that you can activate that automatically migrates all of your images to WordPress.com’s content delivery network.
With that one click, all of your images are now served from a free CDN that will speed up performance world wide and offload traffic from your Azure Web Site subscription. For those of you running large scale or “premium” WordPress sites on Azure, this may be one way to avoid having to scale up your hosting plan in order to maintain performance around the world.