For Outlook 2007 to work with Office 365, the client required a patch. It is provided by Microsoft and can be downloaded here,
1. Run the downloaded .exe file.
2. Login with your email address and password.
3. Click Continue, then click I Accept.
4. The patch will install, then click Finish.
5. Edit the Outlook Profile.
Editing the Outlook Profile
1. Open the Control Panel.
Windows 7: Start > Control Panel
Windows 8: Start (Bottom right of the screen) > Type Control panel. Click Control Panel.
Note: The "View By:" setting (top right) might need to be changed to Large icon or Small Icons.
2. Click Mail (32-bit)
3. Click Show Profiles.
4. Select your profile, then click Properties.
5. Click Email Accounts.
6. Double click the email account from the list
7. Change the server address to, outlook.office365.com
8. Click More Settings...
9. Select the Security Tab.
10. Change Logon network security: to Anonymous Authentication.
11. Select the Connection tab.
12 Click Exchange Proxy Settings...
13. Change the following Field
Check Connect using SSL only
Check Only connect to proxy servers that this pricipal name i their certificate: msstd:outlook.com
14. Click OK. Then OK again.
15. Click Check Name.
16. Type your email address and password, Then click OK.
17. Click Next, then Finish.
18. Start Outlook.