On the client you want to log from:
vi /etc/rsyslog.conf

*.* @RemoteSyslogIPAddress:Port

Example:
*.* @172.18.1.50:514

On the remote logging server:
vi /etc/rsyslog.conf

# Begin – Allow remote logging
$ModLoad imudp.so
$UDPServerRun 514
# End – Allow remote logging

Need to send a HUP to the rsyslogd process or

service rsyslog reload