The British actor and rapper, who has roots in Sierra Leone and Ghana, has previously spoken of his desire to develop the film industry in Africa.
"Idris Elba will build a modern studio similar to Hollywood, Nollywood or Bollywood," Zanzibar's investment minister Sharif Ali Sharif said.
He added that the government of Zanzibar had given Elba 80 hectares of land in Fumba, on Unguja island, for the studio.
"I am not sure what we will call it in Zanzibar, whether Zallywood or Zawood, I don't know," Sharif said jokingly while addressing industry participants at the Zanzibar International Film Festival.
Local media say the studio could boost Tanzania's efforts to become a hub for international film production.
The studio plan follows discussions held last year between Elba and Tanzania's President Samia Suluhu Hassan at the World Economic Forum in Davos. | BGNES