Straight out of the box, the current 1.x and 2.x versions of Ghost aren't compatible with the Azure App Service. Ghost-Azure resolves this by providing a production-ready template which can be hosted directly on Azure App Service. In the background, an Azure Function (Ghost-Release-Uploader) makes sure that this repository stays up-to-date with the latest releases of Ghost. Most of the work has been done by Radoslav Gatev who created the deployment template and the release uploader. Due to unknown reasons his repository wasn't being kept up-to-date with the latest releases, so we forked it and ran our own processes.
I documented my installation process, with additional steps to add Sendgrid, SSL, Azure Search, etc. on my blog.
In any case I suggest forking my repository into your own, this to avoid changes I make to my repository to negatively impact your installation.
Azure App Service Deployment Center
More info on Microsoft Docs