use scp:
Secure copy - Wikipedia, the free encyclopedia
(examples included in the wiki link)
don't forgett to copy apache or nginx configs.
make sure, that the new server has the same programs installed, as the old ones (if you need s.th. special)
don't forget to restart the services, after changing the config files
ssh default port is 22rsync -avz /old/server/directory -e "ssh -p YOURSSHPORT" root@yournewserverip:/new/server/directory
how to transfer a site from one server to other by shell without cpanel?