If you are currently running Exchange Server 2007 or Exchange Server 2003 and want to manage Office 365 users on-premises, ...

If you are currently running Exchange Server 2007 or Exchange Server 2003 and want to manage Office 365 users on-premises, you will need to upgrade your server to Exchange Server 2010 or higher and then configure an Exchange hybrid deployment. A hybrid deployment offers your organization the ability to extend the feature-rich experience and administrative control you have with your existing on-premises Exchange organization to Office 365.