The 17-year-old, who finished in third place on the BBC talent search earlier this year, will play cabaret performer Sally Bowles in the popular musical.
Barks will appear alongside established performer Wayne Sleep, who is taking on the role of the Emcee.
I'd Do Anything was won by Jodie Prenger in May. She will make her debut as Nancy in the West End revival of Oliver! later this year.
Rachel Tucker, another former Nancy hopeful, has also been offered theatre work since appearing on the show. She recently signed up to play a lead role in West End musical We Will Rock You.