After years of grooming, John Elkann is stepping up to take a high-profile role at Fiat SpA, the auto maker at the center of the Agnelli family's sprawling industrial dynasty.

Mr. Elkann, a great-great-grandson of Giovanni Agnelli, who helped found Fiat in 1899, will be appointed chairman when Fiat's board meets Wednesday, Fiat Chief Executive Sergio Marchionne told a news conference in Turin Tuesday. Mr. Elkann will succeed Luca Cordero di Montezemolo, who told the news conference he will remain on Fiat's board and keep his position as chairman of Fiat-owned Ferrari.