Yes you can do this. If you O365 account is enabled with the license. Simply sign out of your existing office and then sign in with your work account.
- Open a single Office App (Word, Excel, etc) and close the others.
- Click File to go to Stage area
- Click "Account' in left hand menu
- Under "User Information" click Sign Out.
- Restart the application then sign in with your work account.
There is a "switch account" option there - You can try that, but I have 100% success with the above method.
Now on your personal account you may want to sign into O365 and deactivate the license. If you are using the personal O365 subscription keep in mind that this also grants you storage for OneDrive personal and Skype minutes. If you use those don't cancel the subscription. If you don't - and all you used was Office, than it's probably worth canceling as you won't be using that feature.
Is the work version also an online-activated version like Office 365 Business? – Daniel B – 2015-09-17T09:27:55.167
It says MS Office 365 ProPlus Subscription Product on the Account page in Word - that's my work version – Rob Sedgwick – 2015-09-17T09:36:25.130
1Office 365 activation is based on what Microsoft Account you are logged into. If you work will allow you to log into their Office 365 account they have assigned for your use, you can do so, easily enough. You obviously would need to install the same version of Office 365 in order to do so. – Ramhound – 2015-09-17T15:03:35.420