UPDATE: Apple slightly changed the Smart Cover design in October 2011. The magnet that controls the sleep/wake function has been reversed in polarity to prevent accidental triggering of the switch. If your Smart Cover is older than this, it may not work with the new iPad. There are reports of Apple Stores exchanging non-working covers for customers but this has not been confirmed.
The 3rd generation iPad is designed to use existing Apple Smart covers. Yes, the Smart Cover you currently use on the iPad 2 works just fine on the new iPad 3.
The magnets in the bezel of the new iPad are configured precisely to utilize the iPad 2 Smart Cover, despite the slight increase in thickness.