See:
iTunes: Moving Your iTunes Music Folder
IMPORTANT: do not delete the iTunes folder or the preference files it contains from your boot hard drive; delete ONLY the tracks themselves (i.e. the contents of the old iTunes Music folder).
You can also just drag the entire iTunes folder (the
entire folder,
not just the iTunes Music folder) to your desired location. Then hold down the Option key while launching iTunes. You'll be given a dialog box where you can select the iTunes library you want to use. Navigate to and select the iTunes folder in it's new location. Note that this procedure assumes that all of your tracks are contained in the iTunes Music folder. If they're scattered around your volumes, moving them becomes much more complex.
In either case, don't delete the tracks from the old location until you've confirmed that they're working correctly from the external drive.