Yes. Once you have all your files backed up, simply upload them to the new server. After that, you will also need to backup the database and move it to the new server also. You then need to modify the configuration.php file on the root with the new db server settings: UN, Host & Password. If you have problems, there is a component called JPack that makes this much easier.
After you have the entire site moved you may have to go through and modify folder permissions before you can install any new components, modules or plugins.