With the release of Office 2016, Microsoft has also released the Office 2016 Deployment Tool (download here).
New features for Office Deployment Tool:
The download of Office Deployment Tool contains a sample configuration.xml. Check out the Reference for Click-to-Run configuration.xml file for a complete reference on what can be configured.
Aside of some minor additional options to the configuration XML, using the Office Deployment Tool hasn't change very much, so this article about how to configure and use Office Deployment Tool for Office 365 is still valid.
More information about updating to Office 2016 for Office 365 ProPlus can be found in this article on TechNet.
The new version of Office Deployment Tool can only be used to install Office 2016. If you wish to install the Office 2013 version of Office 365 ProPlus, you have to use the previous version of Office Deployment Tool.
Updates for Office 2013 through Office 365 Click-to-Run will continue until September 2016, after which only Office 2016 will be supported and receive updates.