Go to iTunes Menu > Preferences > Advanced (Tab).
In there you can change the iTunes Media folder location. Make sure you have your new drive connected first and select the location on the new drive you want to move it to. Press OK.
IIRC it tries to move your files immediately. If not, after clicking OK in the Preferences window, go to File > Library > Organize Library. In here, check "Consolidate files". Then hit OK to start the process. It will start moving all your files from ~/Music/iTunes/iTunes Media to the new location you selected. Even if it does something after you change the location, you might want to consolidate just to be safe.
This process will keep your library intact, and relink all the items in your library to the new copies of the files. However, keep in mind that the iTunes library file itself (very small) will still be stored at ~/Music/iTunes/iTunes Library.itl. You DO NOT want to delete that.
It leaves behind the original media files at ~/Music/iTunes/iTunes Media. After verifying that the copy was successful, you'll want to delete that folder, not the entire ~/Music/iTunes folder.