The biopic, which is in development at studio A24 - known for gruesome films including Midsommar and Heriditary - will be based on Walter Isaacson's authorized biography of Musk, which was released in September.
Variety reports there was 'heated competition' to option the biography from studios and filmmakers.
Musk addressed the news on X on Friday, writing in response to a post by X News Daily: 'Glad Darren is doing it. He is one of the best.'
The author, who previously wrote an exhaustive biography of the equally controversial Apple co-founder Steve Jobs, was given unprecedented access to the Tesla and SpaceX owner over more than two years.
Isaacson observed Musk go about his daily life and conducted interviews with him and members of his family to build a picture of his life.
His book chronicles Musk's rise to fame through his SpaceX ventures, selling a million cars through Tesla, and becoming the richest man alive.