Log into your cPanel -> phpMyAdmin -> locate your Magento database and click the core_config_data table. There will be two fields containing your domain, which you must edit by putting the new domain.
web/unsecure/base_url
web/secure/base_url
*Note that if you wish to access your Magento with www, type the new domain with the www.
Once that is done, you need to clean your Magento Cache. To do that, log into your cPanel -> File Manager -> and look for /var/cache/ directory. Then delete the folders in the cache directory.
