Consider you already have 2 Linux server then open terminal or ssh at the new Linux server.
type command below
#rsync -av --exclude=/boot-e ssh username@oldserverhost:/(source) /(destination)
or standard rsync
#rsync -av -e ssh username@oldserverhost:/home/old_home/ /home/new_home/
password will be prom then enter password.
i exclude boot file because it need difficult configuration. You also can exclude the folder you want to rsync too such as /root /home /lib or anything else.
After finish the transferring data, your have to reconfigure, the Ip address,hostname or any necessary file need such as apache, mysql or others that you use.
*Ip tables or firewall at linux sometime need to stop to running the application.