1. Sign into portal.Office.com and launch any online office application.
2. At the bottom left side of the page, click Add a place and then check the box next to Dropbox. This will add Dropbox as a new save location.
3. Click on the Open from Dropbox new link and then sign in with your Dropbox username and password.
Once connected, you can click on the Open from Dropbox link to open Office files or save files to Dropbox from Office Online.
1. Save an Office file to Dropbox or the Dropbox sub-folder you want to use as your default for Office files by going to File > Save As and then browsing to that folder.
2. Return to the File > Save As menu and locate your Dropbox folder in the right column.
3. Hover over the folder until you see the pushpin icon and click it to pin that folder to your Save As menu.
Next time you go to save a file, you can choose that pinned folder rather than having to wade through your computer directory to your Dropbox folder. It's not a perfect connectivity solution, but until there's another workaround for Office 2016 or Dropbox gets better integration with Office on the desktop, this is the simplest solution.