From: About your Apple ID email addresses - Apple Support
Add or change a rescue [for most people called a notification address] email address
1. Sign in to appleid.apple.com.
2. Select Sign-In and Security.
3. Select Rescue Email. You might be asked to answer one or more security questions or enter your Apple ID password before you continue.
4. To add a rescue email address, select Add email. Then enter your rescue email address, then select Save changes. We send a verification to that address.
5. To change a rescue email address, enter the new address. We send a verification to that address.
6. Enter the verification code and click Continue.
If at any stage you don't get an expected verification see: If you didn't receive your verification or reset email - Apple Support