Change my Apple ID email address on iCloud account
Go to https://appleid.apple.com, click Manage my Apple ID and sign in with your current iCloud ID.  

Tap edit next to the primary email account, tap Edit, change it back to your old email address and save the change.  

Then edit the name of the account to change it back to your old email address.  You can now use your current password to turn off Find My iPhone on your device, even though it prompts you for the password for your old account ID. 

Then go to Settings > iCloud, tap Delete Account and choose Delete from My iDevice when prompted (your iCloud data will still be in iCloud).  

Next, go back to https://appleid.apple.com and change your primary email address and iCloud ID name back to the way it was.  Now you can go to Settings > iCloud and sign in with your current iCloud ID and password.