It is a little bit strange but you have to add it as a new domain (after you have completed the initial domain setup) to your Office 365 Instance. This domain will actually be:
You will pass quite fast over the verification part and then you have to specify the domain services. This time please choose only SharePoint Online.
Then click next and go to the SharePoint Online Administration Center.
Add a new public web site. Be aware that you can add only ONE public website per Office 365 Instance. You can select the public URL from the URL drop down.
Select the newly created site collection and then from the ribbon click on DNS Information.
Take this information and use it to create a CNAME record in the DNS Server at your registrar. The CNAME should look like
www-or-some-other-name.your-already-registered-domain.com CNAME dns-information-url
As soos as this is done you would be able to access your SharePoint online public site using the public web address.
As an example: all screen shots used to create this post are form my SharePoint Online Website’s – http://sharepoint.denisstadler.com – creation process.
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