The Wire star will play Professor Henry Higgins in the musical, while young actress Carly Bawden has been cast as Eliza Doolittle.
West has never sung onstage, but director Daniel Evans is confident the Brit will be able to pull it off.
He tells Britain's Daily Mail, "Higgins was made for him. Dominic has the temperament for it, and he has the class... Dominic's an amazing actor. He'll be thorough, he'll be playful and he'll sing as much as he wants to sing and we'll discover what we need in rehearsals."
West's My Fair Lady will run at the Crucible Theatre in his native Sheffield, England from 12 December (12) until 26 January (13).