Migrate Google Authenticator to new iPhone 7
First, two things.


Keep your backup codes
Keep your old phone


From what I have found, you will need to use the "change" option on each of your 2-step verification enabled apps/sites. This will most likely require you to log into each account using your current 2-step verification process first (hence the use of backup codes or your old phone).

If you have trouble transferring the authenticator application over, try the following tutorial.
https://www.brianckeegan.com/2016/09/how-to-transfer-googles-2-factor-authentication-to-a-new-iphone/