Sure, time machine can do this. Open the time machine preferences and press the options button. That will show a list of everything that time machine is *not* backing up. If your external drive appears on that list, select it and press the minus button to remove it from the exclusion list.
IIRC, in the past your external disks were automatically added to the exclusion list. But I don't think that is the case anymore. I have time machine backing up an external disk on the Mac that I got last summer, and I don't think I had to do anything for that to happen.
To confirm that it works, open a window to your external disk, then click the time machine icon in the menu bar (looks like a little clock) and choose "enter time machine". You should be able to browse through all the backups for the external disk.