You are getting an error message because your primary email cannot be the same as your rescue email. You have to first change your rescue email.
I just went through this. A source of confusion is that the instructions are not clear, and the option to change your rescue email is not easy to find.
Go to manage Apple ID (https://appleid.apple.com/account/manage), and in the left navigation to password and security. You need to enter answers to your security questions before you can go through. If you forgot the answers, there's a link to send security questions reset information to your rescue email.
Once you have entered the answers to the security questions, you can change your rescue email - you'll have to enter one different from the main email, and you'll have to validate.
Once this done, you can set your current email as your primary email, and then set it as your appleID.
Update: It was mentioned below, but worth adding it here to save headaches. Turn off Find my phone in all devices that are signed in to icloud. Otherwise, you won't be able to sign out, as your device will be signed to an account (used id) that does not exist. Suggest making a backup first and then signing off from iCloud. Make the ID change once all devices are signed off.
If you forget to do that, you will either have to restore the device, or will have at a later time to change your id back to the old email, log off the device, and then change it back to the new one.