I have a Visual Studio 2017 solution with both an ASP.NET Web Application project (called UI) and an Azure WebJob project (called WebJobs). I have configured both to deploy
All you have to do is create the WebJob project by right clicking on your Web App and choosing:
Add / New Azure WebJob project
Or if you already have a WebJobs project in the solution:
Add / Existing WebJob project
Once you do that, publishing the Web App automatically publishes the WebJob where it belongs. It all happens in a single zip file, and there is nothing special to do in VSTS. Do not try to publish the WebJob project individually once you do that.
With webjob associated to web app, the webjob is included in the web app package, so you just need to deploy web app to azure app service.
It will generate webjob’s package too during publishing (that why there are two zip files), but you just need to specify web app package in Azure App Service deploy task. (Check Publish using Web Deploy option)