Hope beat 17-year-old Sophie Evans, who finished in second place during Saturday's two live shows, and 22-year-old Lauren Samuels, who came third.
It was also revealed on Saturday that Hope's co-star Toto will be played by a Mini Schnauzer called Dave, or "Dangerous Dave" as he is known to his owner.
On winning the show, Hope thanked the audience, backstage crew, judging panel and the other girls, before adding: "All I can say is thank you but it really does come from in here. It feels like not enough but I am just so grateful. We all are for this amazing opportunity."
Lloyd Webber said he was "really pleased" with the result. "You're the most fantastic, talented kid with a huge future ahead," he said. "Now the hard work starts but my goodness me, you can act from the soul and that is something that's very special."
Hope’s single, “Over the Rainbow”, is now available to download, with a physical copy released on 31 May.
The Wizard of Oz, best known from the 1939 Hollywood film starring Judy Garland as Dorothy, is being “totally reconceived” and will include new songs written by Lloyd Webber. It begins performances at the Palladium on 7 February 2011, with press night on 1 March.
CATCH UP: Our Over the Rainbow blog has been following all the action from day one of the contest.