Upgrade Automatically to Office 2016 from the Menu Bar Notification
If you have an Office 365 subscription, are currently running Office 2013, and have automatic Windows and Microsoft software updates enabled, you might get an upgrade notification from within Office to upgrade to 2016. Click on the notification and follow the prompts to update to the latest version.
However, Office 2016 is still rolling out and it could take a few weeks to get the upgrade notification. This chart from the Office 365 community shows the upgrade timeline based on Office 365 plans or versions (the table is blank for Office 365 Home, Personal, or University but you can upgrade to Office 2016 now with those plans):