I am guessing you just have media on the new drive, not your whole iTunes library (all the library files and folders in an iTunes folder).
What are the iTunes library files? - http://support.apple.com/kb/HT1660
More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html
iTunes does not like it when you move media to a new location, especially not to another drive. You have to let it do it so it can keep track of things.
1) Connect both drives. Use iTunes preferences to change the location of the media folder and let iTunes consolidate media to the new drive. iTunes 10 for Mac: Consolidate your iTunes library - http://support.apple.com/kb/PH990 and iTunes for Mac: Moving your iTunes Media folder - http://support.apple.com/kb/HT1449
2) Assuming the folder structure is pretty much identical to the one on the old drive, you can: A) Find one song on the new drive and hopefully iTunes can find the others (say yes when it asks if you want it to do this), or B) Give the new drive the exact same name as the old one and hope it tricks iTunes into thinking it is the same drive.
By the way, this is not a "backup drive". A backup is a second copy you keep for when your main drive fails. This drive is being used actively for your primary iTunes use. When this new drive fails you will, of course, lose your whole iTunes collection unless you truly do have a real backup drive.