I had this issue too, took me weeks to get this working again and many uninstalls and reinstalls that did nothing. Apple support couldn't help, Microsoft couldn't help either. I think the trick is to COMPLETELY remove Outlook then reinstall. But this is trickier than you think. Try these steps and reply back if this works for you:
1. Log out of iCloud
2. Uninstall iCloud
3. Uninstall Office 2016
4. In control panel, open Mail32 and delete all profiles
5. Open regedit and delete the folder [HKEY_CURRENT_USER\SOFTWARE\Microsoft\Office]
6. Rename the Office folder to OfficeBackup in C:\Users\[your user name]\AppData\Local\Microsoft\Office
7. Rename the Office folder to OfficeBackup in C:\Users\[your user name]\AppData\Roaming\Microsoft\Office
8. Install Office - set up to work without an account, or if you have one add your other account such as Exchange/gmail etc
9. Install iCloud and click to get mail and contacts working in Outlook
10. Open Outlook and it should work again. Remember if you have two factor authentication you will need to go into your iCloud accounts/manage page and create and use an app specific password or Outlook will keep asking you for your iCloud password
Any local pst files etc that you might need to reconnect will be in the Roaming backup folder you made earlier if you need to grab them back.
Good luck!