it was smooth for me, I went to this address:

https://appleid.apple.com/account/manage

• Signed in with my existing gmail Apple ID
• clicked the Apple ID link to change my address
• entered my @me.com address
• grabbed the verification code from my email

and that was pretty much it, now I can sign in with my @me address for Apple ID

I didn’t even need to log out on any of my devices, they display the @me address in the settings as my Apple ID instead of the gmail address