Ответ найден здесь: http://www.exim.org/exim-html-4.50/doc/html/FAQ_3.html#TOC124 Q0303: How do I configure Exim to send all messages to a central server? I don't want to do any local deliveries at all on this host.
A0303: Use this as your first and only router:
Code
send_to_gateway:
driver = manualroute
transport = remote_smtp
route_list = * central.server.host
