Set up Varnish to proxy to a different host

varnish-host-proxy.vcl

# Add this code to your VCL configuration.
#
# I assume a default backend has already been configured.

# If different from the default backend, add one for the host to proxy to. Note that these
# values are just examples.
backend proxy_host {
  .host = "proxy_host.dev";
  .port = "8080";
}

# This is where the magic happens. We detect an incoming request and proxy it to the other
# host.
# Note that is a very bare bones setup, purely for illustrating you to proxy.
sub vcl_recv {
  if (req.http.host ~ "^incoming_host\.dev") {
    set req.http.X-Forwarded-Host = req.http.host;
    set req.http.host = "proxy_host.dev";
    set req.backend = proxy_host;
  }

  return (pass);
}