To authenticate users on your system using Office365 account, just use this guide: ASP.NET MVC Identity Walkthrough with Microsoft Account Authentication .
But it will not work well as they expect. Even though users authenticate with Office365, when they access your system, they will have to authenticate using the same credentials. However, nothing that a% of% "Remember me" does not solve. :)
Finally, you can not continue to use the same system password and use Office365 authentication. If you are going to use Office365, it will manage the endorsements, not your system anymore.
If you want an easy-to-use code, just create a new ASP.NET MVC project in Visual Studio with Forms Authentication template. Then go to the controller checkbox
and see the implementations.
In my GitHub you have an example with Isolation of ASP.NET Identity , it may help.