This should be an easy fix:

1. login to your wordpress dashboard
2. left menu select “Settings” –> “General”
3. then change both “WordPress Address (URL)” and “Site Address (URL)” from your IP to your domain name (don’t forget to also put http:// in front of your domain, or https:// if you have SSL) and hit “save changes”
4. goto “Settings” –> “Permalinks” and click on “save changes”

Voila, you should be good to go :)

And don’t forget…
Your domain must resolv to your IP (DNS).

Great answer @sugarhill

It would be great if @julianlampert can elaborate on his answer!