You need to go into your new database and change the site url and home url to the new address. I suggest NOT doing this through phpmyadmin or the WP dashboard (using plugins) though as it will cause some problems. Plugins May work, but if wordpress hangs or times out or any number of things you could have a bigger problem.
I recommend is using Search & Replace DB, a free tool by Interconnect, to replace any instances of the host name in the database. It will handle setting the serialized data correctly for you. and it works OUTSIDE of the WordPress system.
First make sure that your wp-config is for the right database.
Go get this tool: https://interconnectit.com/products/search-and-replace-for-wordpress-databases/
Upload it into your www/ folder. (I usually rename the search and replace folder to SRDB.)
Now navigate to your site with the SRDB at the end on the NEW url. (www.example.com/SRDB) and the top two lines you’ll see a search field and a replace field. (if you get a db connection error here, double check the wp-config to ensure that it has the right credentials).
In the search field, place your old site address.
In the replace field, place your new url.
Hit live run.
ONLY do this after ensuring you’re on your new url and that SRDB has loaded into your new database.
Remove the SRDB folder when you are done.