The former X Factor contestant has been hired to play the title character in the Jim Cartwright-penned production, which will open at he Vaudeville Theatre on October 8.
Producer Nica Burns said: "With this wonderful play, you have to find your Little Voice first. To find someone of the right age - just 18 - who is as special as Diana Vickers is a gift.
"Having found our perfect Little Voice, I was delighted that the outstanding actress Lesley Sharp agreed to play her mother Mari and the charismatic actor Marc Warren, Ray Say."
She added: "When Marc and Lesley first walked on stage together, the chemistry between them was instant. This is a terrific play and a great night out."
Vickers has said that she was "so lucky" to get the part in "such an amazing play".