Update your database

go to “PHPMyAdmin” and log into your PrestaShop database. Go to the table “ps_configuration” and locate the records for PS_SHOP_DOMAIN and PS_SHOP_DOMAIN_SSL. Change these to the new domain name. Check the configuration table for any other entries that contain the old domain name and change accordingly.

Note:Beckup .htaccess file from root

Updating your config settings

Via FTP or the file manager in cPanel, modify the PHP file /config/settings.inc.php. Look for the entry for PS_BASE_URI__ and modify as necessary. For a shop located in the root, it should read:
// generate->generate .htaccess”.

Enabling SSL

If your site has a full SSL Certificate, then you can also enable this via your PS admin under “Preferences page -> Enable SSL: Yes”.
Please note that PrestaShop won’t work with our Shared SSL as the SEO URLs rewrite rules don’t work with the server paths. For PS shops, you either need to have a Dedicated IP & your own Full SSL Certificate or you need to disable SSL.

For Reference: http://www.prestashop.com/forums/topic/169435-move-prestashop-to-new-domain/

 e.g. (assuming the DB_PREFIX is 'ps_') :
UPDATE `ps_configuration` SET `value` = '0' WHERE `name` = 'PS_CIPHER_ALGORITHM';