How do I change iCloud to my new Apple ID?

I no longer have the email address that I originally setup as my Apple ID & iCloud, so I changed it through the Apple website. Now my iPhone 4 keeps asking me to login into iCloud with my old Apple ID (which no longer works). How do I change iCloud to my new Apple ID?

I have been able to change the Apple ID in "Settings>iTunes & App Store" but the Apple ID is greyed-out in the iCloud settings.

The phone repeatedly asks me to sign in to iCloud and asks for the password for my old Apple ID. I can't login and when I hit 'Cancel' the login prompt returns again in approx 3 seconds. This happens no matter what I am doing, txt, email, browsing. It is almost unbearable!

Any help would be greatly appreciated.

Cheers,

Greg