WordPress charges for each domain attached to a blog. That is a bit much when you consider .net, .org, .whatever domains that are used on top of the .com domain most use. To get the use out of a single domain, a permanent redirect can be used. Since Azure has a fixed price, invariant of how many domains you host there; it can be used for the permanent redirect.

Prerequisites

• An Azure App Service app on a paid tier (Shared or better - Free/Shared plans cannot map custom domains).
• A domain you own with access to its DNS records at the registrar.

Map the domain

In your registrar’s DNS settings, create a CNAME record pointing www (or the subdomain you want) at <your-app>.azurewebsites.net. For the apex domain, use the A record Azure shows under the app’s Custom domains blade instead (CNAME at the apex is not supported by most registrars).

Then in the portal: App Service > Custom domains > Add hostname, validate, and let Azure wire up the mapping.

Add the redirect

Open the Kudu console for the app (https://<your-app>.scm.azurewebsites.net), navigate to site -> wwwroot, and edit (or create) web.config:

<?xml version="1.0" encoding="utf-8" ?>
<configuration>
    <system.webServer>
        <rewrite>
            <rules>
                <rule name="Redirect old-domain to new-domain" stopProcessing="true">
                    <match url=".*" />
                    <action type="Redirect" url="http://<<appdomain>>/{R:0}" redirectType="Permanent" />
                </rule>              
            </rules>
        </rewrite>
    </system.webServer>
</configuration>

Replace <<appdomain>> with the domain you wish to redirect to. The {R:0} preserves the original path, so deep links like /2018/some-post/ land on the same path at the new domain - which is exactly what a permanent (301) redirect should do for search engines that are still holding onto the old URLs.