After your outlook.com account is moved to the new Outlook.com server you'll need to remove the Outlook Connector account from Outlook 2010 and add it back using auto account setup.
You'll need to use auto account setup to add the account to Outlook. You cannot manually add the account to Outlook if you want it set up as an Exchange Account.
If your outlook.com account does not have an Outlook.com address, you'll need to add an Outlook.com alias to it.
If Outlook won't accept your password, click Cancel on the password dialog. You should see an error message:
The connection to Microsoft exchange is unavailable. Outlook must be online or connected to complete this action.
After you click OK on this dialog you'll see the check account dialog, where your email address will be preceded by =SMTP. This indicates that you don't have current Office updates installed.
You will need to install the updates before you can completely set up the account in Outlook.
After all updates are installed you should have version 14.0.7173.5000 (or newer). Auto account setup will work and add your account Outlook. You must have at least 14.0.6129.5000 installed and it's highly recommended you have all updates installed.