Google accounts on my Galaxy S4
Important: Sync your old Google account data between your phone and Google before starting with the following instructions.

You should log in to your old Google account, and then go to Google Takeout, where there are tools to export your account information to an archive (and even you'll be able to transfer all your Google+ circles to your new account).



To move contacts and other info from the old account to the new one, follow the instructions from this article.

Also you can go to Data tools settings page, where you'll find how to delete your old account, in the section Account management. Good luck.