There is no specific way to run your code in Azure. You have lots of choices, and which you choose is really up to you (and a matter of opinion). But, objectively speaking:
- Install your service as you always have, in a Windows Server VM
- Run your code, without the Windows Service wrapper, in a VM (either Windows or Linux, depending on language)
- Pull your core code out of the service, and run it within a web/worker role (cloud service).
- Run your code in a WebJob.
- Run your code in a Web App (you'd need to add some way to get to it, like a REST API sitting in front of it)
I see that @Neil suggested Service Fabric in his answer. That works too, except you'll need to learn about Service Fabric in general, since it works a bit differently.
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