The following instructions step through the process of configuring your Office 365 Exchange Online account with Apple Mail for Mac OS X 10.9 - 10.10.
Open Apple Mail.
*Note: If this is your first time opening Mail, go to step 3.
From the Mail drop-down menu, select Add Account...
Select Exchange, then click Continue.
Enter a display name for your account in the Name field.
Apple Mail will produce an error. Select Continue on the error.
Choose the apps you wish to sync, then click Done.
Next, you'll want to add your email alias (e.g. firstname.lastname@example.org) to your Account in Apple mail. This will prevent you from receiving your own message when you click reply all in an email message.
Select the Mail drop down menu, then choose Preferences.
Select Accounts icon from the toolbar, if you have more than one account listed, be sure to select the Exchange account, then in the Outgoing Mail Server drop-down menu, select None.
Click the General icon in the toolbar to open a dialog box that will save changes.
Again in the Accounts section, select the Alias drop-down and choose Edit Aliases.
In the Outgoing Mail Server drop-down menu, select Exchange. Click the General icon in the toolbar to save changes, then close the preferences window.