Depends. Are these zombies killable? As in, if I blow one's head off, will it lie in a bloody heap on the ground and not get up again?
If so, then yeah. Eventually, after a long enough period of time, the zombies will all be killed. It may take a really freaking long time of people shooting them and them eating each other when their normal food source (live people) runs out, but they will eventually die out. Once that happens, it should be easy enough to dispose of all the bodies (yay fire), clean away the blood, and start again. You have to be absolutely sure that every last zombie is dead first though, as well as any source that can transmit the zombie condition to others.
Eventually, the zombie epidemic would be added to the history books right alongside the black death, and people will carry on with their lives not really worrying about zombies anymore.