If the new server is on the same IP network than the old one, Check for IP-Masquerading in google or the IP-tables man pages.
Masquerading should be done on the Firewall.
If your new server is at a different site or IP network, I don’t think there is an easy solution.
If you are using host names to reach the server, make a static host entry in your /etc/hosts (linux) or hosts file somewhere under the windows directory, pointing to the new server’s ip address.