Microsoft has been running technical previews of App Service on Azure Stack for more than a year and just yesterday announced its general availability (along with Azure Functions) on Azure Stack.

Functions running on Linux dedicated (App Service Plan) or Linux Elastic Premium SKU are always container based. The exact image to be used by the function app is controlled by the SiteConfig entry ...

Specifically, this is the first version of Azure Stack to offer support for Azure Functions ... the release also includes the Azure App Service, Microsoft’s cloud tools for quickly developing ...