The NBC series is inspired by the novels of writer Thomas Harris.
> Gina Torres on 'Hannibal' TV series: 'It is chilling'
Fuller broke the news of the series premiere date on Twitter, writing: "#Hannibal requests the honour of your presence for dinner Thursday April 4 10PM @NBC -- Saving you a place at the table."
Fuller also revealed that Eddie Izzard has been on set, posting a picture of the two together and writing: "Always hungry for more @eddieizzard on #HANNIBAL - here we plot our next course."
Izzard will reportedly play an asylum inmate who claims that he is an infamous serial killer.
> Mads Mikkelsen on 'Hannibal' role: 'It's bloody and gruesome'
The show will explore the early relationship between Dr Hannibal Lecter and a criminal profiler, special agent Will Graham.
Lecter will be played by Casino Royale star Mads Mikkelsen, with Hugh Dancy (The Big C) in the role of the Agent Graham. Caroline Dhavernas (Devil), Lara Jean Chorostecki (Copper), Gina Torres (Suits) and Laurence Fishburne (The Matrix) also feature in the series.
Fuller is an executive producer on the thriller, along with Martha De Laurentiis, Katie O'Connell, Sara Colleton and Jesse Alexander.
15 exciting new TV shows for 2013 - in pictures: