Remove Outlook from the Windows 10 Action Center

In the Settings app, go to System > Notifications & actions, find Outlook and turn off the toggle in the same row.

Personally, I found it better to let the toggle on, click the whole Outlook row and disable just the "Show notifications in action center" toggle on the page that appears. The notifications are still on, but they vanish from the Action center once the notification banner hides.

Right-click on the "Outlook 2013" heading in the Action Center, and select "Turn off notifications for this app".

You can also disable those notifications in Outlook itself. Currently, in Outlook 365, it's under "File" > "Options" > "Mail", section "Message arrival", option "Display a Desktop Alert".