All of our machines here send their mail to a central smarthost running exim4. All the system mails are directed to "root" at some of our machines. What I did was first adding a file /etc/exim4/exim.filter containing this:
# Exim filter if "$h_to:" matches \Nroot@.*\.your\.domain\.de\N then headers add "New-Subject: [System] $h_subject:" headers remove subject headers add "Subject: $h_new-subject:" headers remove new-subject endif
Since we are running Debian, running exim4 in split configuration, I also added the file /etc/exim4/conf.d/main/80_exim4-config_system_filter, containing this:
system_filter = /etc/exim4/exim.filter
After that I had to run update-exim4.conf and /etc/init.d/exim4 reload. Then I was all set up.