Can I use Office365 or Azure AD as master record for Active Directory?

Solution 1:

Short answer: No. However, like @Nathan-C described, you can stand up the required services using Azure Iaas (either DC+DirSync+ADFS or DC+Dircync w/pwd sync) in order to achieve single sign-on between your your Office365 apps and your on-prem apps. You would need to deploy a VPN link between Azure and your local network.

Azure AD is NOT "regular" Active Directory.

Solution 2:

All of this information is old, I just wanted to help someone that was looking for it. Today 10/25/2016 I have 20 or so windows 10 laptops that connect and work with Azure AD services directly. It integrates and works perfectly with o365 and many other "cloud" services from Microsoft.

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Solution 3:

Microsoft recently started offering actual Active Directory services in Azure: https://azure.microsoft.com/en-us/services/active-directory-ds; if you only need centralized authentication, they can fully replace a local AD.