This article covers using Azure Storage static website that is in preview to host a static webpage and creating custom domain on storage account for that webpage. The custom domain used in this scenario is managed by Azure DNS.
Azure Storage now offers static website hosting (Preview), enabling you to deploy cost-effective and scalable modern web applications on Azure. On a static website, webpages contain static content and JavaScript or other client-side code. You can configure a custom domain for accessing blob data in your Azure storage account and use the web endpoint generated as a part of the static websites feature (preview). You can also you map a custom domain and subdomain like www.contoso.com to the blob or web endpoint for your storage account, your users can then access blob data in your storage account using that domain.
Video:
Steps in the above video covers;
Enable Static Website on Storage account
Confirm HTML page on Microsoft Expression
Upload website files to storage account
Confirm website is reachable using endpoint address
https://xxxxxxxxxxx.xxx.web.core.windows.net/
Review steps to setup Custom Domain on storage account.