You should be able to copy the backup folder over, on Windows it's stored under (the directories may be hidden, so you may need to change preferences in Windows Explorer to get them to show) :
Windows Vista, Windows 7, and Windows 8:\Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\
To quickly access the AppData folder, click Start. In the search bar, type %appdata%, then press Return.
Windows XP:\Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\
To quickly access the Application Data folder, click Start, then choose Run. In the search bar, type %appdata%, then click OK.
Copying it into the named folder on the new computer should get it to be automatically recognised and for it to show in the Devices tab in Edit > Preferences on your new iTunes.
And copy your iTunes library over (apps, films, music etc are not included in the actual backup, that just contains your documents, photos, settings etc).
There is this user-tip for syncing to a new computer : https://discussions.apple.com/docs/DOC-3141
Some of the steps on that page have changed slightly (it was written for a previous version of iTunes) :
5, is now File > Devices > Transfer Purchases
6, 'Reset Warnings' at the bottom of the phone's Summary tab in iTunes
7, File > Devices > Back Up
8, File > Devices > Restore from Backup (or Restore Backup button on the Summary tab)