Yes, a USB 3.0 external drive will work on a USB 2.0 port.
Very broadly, if the path from your drive to the system USB port has one non USB 3.0 component,
the interface will fall back to USB 2.0.
USB 3.0 Drive ==> USB 3.0 cable ==> USB 3.0 Port on Device
It's backwards compatible.
Your existing USB 2.0 gear will work on version 3.0 ports and vice versa. You'll be able to maximize your bandwidth when using a USB 3.0 cable with USB 3.0 devices and ports, otherwise plugging a 3.0 device into a 2.0 port or a 2.0 device into 3.0 a port will get you standard USB 2.0 data rates.
Since the new interface has been carefully planned from the start to peacefully co-exist with its predecessor, the connector itself remains mostly the same with the four USB 2.0 contacts in the exact same location as before. Extra pins for the new lanes dedicated to transmit and receive SuperSpeed data are located on the back and only come into contact when mated with a proper USB 3.0 port.
10 things you should know about USB 2.0 and 3.0 from December 2009.
More details at this FAQ and the Wikipedia article on USB.