Hello,
You can use imapsync (see wiki for examples) to sync the accounts from Google to Zimbra.
There is a (commercial) alternative,
Yippiemove. That will do the IMAP sync from their servers behind the scenes. The price may be a bit high for your tastes - not sure if you have a budget for it. I had a very large Gmail box that I wanted to sync over (100,000+ emails, about 6 GB), and it worked quite well. Much better than imapsync at least.
I'm sure there are other alternatives, but those are the two that come to mind.