[SOLVED] moving a WP / ATA installation

I respectfully hope my questio belongs here, but if not, I also hope that the moderator will set me straight.

This is a really basic question but one I have not faced before. I have built a WordPress site using ATA. The project is a makeover. The pre-existing site continues functioning on its original server while I develop on my servere.

So, now that the makeover is done, the client is ready to repont the DNS to my server.

The temp address for development is based on the server IP# and looks omething like this

http://xx.xx.xxx.xx/~site

So where exactly do I change that to http://domainname.com/

Am i right i thinking that the config file in WP is the place to edit?

Feedback please?