Moving to a new domain in the same server

I recently adquired a new domain I would like to use for my old wordpress site. I managed to configure this new domain in the same server and pointing to the main page.

However, after changing the WordPress URL and website URL fields under Settings, the layout for the site breaks. It’s like the theme I’m using gets corrupted.

What is the correct way of switching from one domain to another?
I looked at http://codex.wordpress.org/Moving_WordPress but this doesn’t mention the case when both domains are under the same server.

Thanks for your help,

You are facing the error because the database tables have old domain stored in all tables and post meta data.

You need to replace all instances of previous domain with the new one in the database, the following link will help:

https://interconnectit.com/products/search-and-replace-for-wordpress-databases/

You should also update your permalinks after the above process.