If you keep the same config, i.e. node names do not change in your /etc/munin/munin.conf file, then it's pretty much just a matter of moving across the contents of /var/lib/munin, which is usually where the RRD files are kept. The graphs will be re-generated from the RRD data so you don't really need those.
If your old and new server are not the same architecture, then you need to perform a dump and restore process on the RRD files rather than just copying them across, because the binary data contained in the files is different between 32-bit and 64-bit systems. In our case we decided to just stick with a regular x86 setup for the new box, so I can't comment on how well this works, but I found the following article which looks like it should work just fine: munin: migration from a 32bit to a 64bit host.
Not sure if this applies to you, but having recently done this, I also had to migrate the contents of /etc/munin/plugin-conf.d, as it contained some snmp-related stuff related to the munin-node on the old server. You might also want to look at /usr/share/munin/plugins and /etc/munin/plugins for anything custom that has been accumulated over the years.