Directed and choreographed by Craig Revel Horwood, the new production will open at the Curve Leicester on 30th July 2016.
Musical supervision and arrangements are by Sarah Travis. Further casting and tour dates are to be announced.
Burke said: "“I’m over the moon to be given the opportunity to play the wonderful Deloris in Sister Act. It’s such an iconic role and a part I’ve always wanted to play. I love touring the UK and I’m thrilled to be working with Craig and his amazing creative team. I can’t wait to get started!"
Revel Horwood said: “I am truly thrilled that Alexandra is going to be our leading lady in this all new production of Sister Act at Curve. Alexandra is such a fantastic singer and actress that I know she is going to be amazing. I couldn’t think of anyone better to play the role of the smart and funny Deloris.’
Burke can currently be seen starring as Rachel Marron in the national tour of The Bodyguard, a role the X Factor winner previously played in the West End.