Darabont's deputy Glen Mazzara, who previously wrote an episode for the show's first season, is to take over from the departing showrunner, as was also widely rumoured.
Darabont may still play some part in the horror drama, according to the network.
"AMC is grateful to executive producer, writer and pilot director Frank Darabont whose contributions to the success of The Walking Dead are innumerable," the broadcaster said in a statement. "We continue to discuss his ongoing role with the series."
Robert Kirkman, the creator of the Walking Dead graphic novels, was confirmed to be remaining in his role as executive producer and writer, while Gale Anne Hurd will also stay on as executive producer.
Darabont had previously spoken to fans at this year's San Diego Comic-Con, where he admitted that he had "needed a little time off" before planning the show's second season.
The Walking Dead's second season premieres on October 16 at 9/8c on AMC in the US. It will air in the UK on FX in late 2011.
Watch the trailer for season two of The Walking Dead below: