Transfer a Wordpress website from one HostGator account to another one.

I have a wordpress website that I created on my temporary hosting account and I need it transferred to a new web hosting account that I just created specifically for the site. Both accounts are Hostgator accounts and I have the necessary logins for both Cpanels. This will be very straightforward and simple. Ideally, I would just go into WP and export the XML data from the existing website and re-import that onto a fresh install of WP on the new website. That did not work with this particular website, so I need the entire site moved from the host it's presently on (and loading fine) to the new host.