Took this information from a recent question of the same topc in our support system:
Here is some more detailed information for you...I'm running through this procedure using 3.1.3, so you'll probably want to upgrade your current box before making the move.
1. Upgrade current box to 3.1.3
2. Set up second box in parallel...mine has its own DNS server so it thinks its authoritative for itself. The new box has the same hostname as the old box, though a different IP address. When installing Zimbra, make sure you set up the same admin account. It's also nice to use the same spam and notspam accounts, just to keep the transition smooth. After the installation is complete, the new box will have the admin account and two spam accounts looking identical to the first box.
3. Back up the first box. zmbackup -f -a all
4. Tar up the backup directory. DO NOT JUST GET THE SESSION. There are some shared blobs that are used for multiple backups, and you don't want to miss those. It's easiest to tar up the whole deal and FTP or SCP it over to the new box.
5. Take down the first box. Untar the backup tarfile on the second box into the /opt/zimbra/backup directory. You want this to look the same as the backup directory on the first box.
6. Run 'zmrestoreldap' to restore the directory. This needs to be run with the Zimbra services down. This will load the distribution lists and account info.
7. 'zmrestore -a all -c -rf' What this is doing is restoring all accounts, including their entries in directory services, skipping any errors (like the admin and spam accounts), and only restoring from the full backup. This prevents the new box from trying to run any redo logs that it has sitting around.
8. 'zmrestore -sys' This will restore any local system configuration changes that were present on the old box. You could probably also do this by adding -sys to the zmrestore in step 7, but I didn't want to complicate things.
When this is all done, the new box should be ready to go up in place of the old one. You can change its IP address over and switch it back to using standard DNS, and move the old box fully offline.
This worked okay for me in testing, but obviously you'll want to run it through and check out the accounts before bringing the old box totally offline. | 
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