Erivo, who is joined in the cast by Jon Robyns (Spamalot) as Adam Nehemiah, recently appeared in I Can't Sing! at the Palladium and The Color Purple at the Menier Chocolate Factory.
The show, which is based on the book by Sherley Anne Williams, is set in 1846 and follows two young women - one white, one black - on their journey to acceptance in racially divided southern America.
Ahrens and Flaherty's other award-winning collaborations include Ragtime, Once On This Island, Seussical and Rocky The Musical.
Directed by Andrew Keates, Dessa Rose runs from 31 July to 30 August 2014 (previews from 29 July).
Ahead of Dessa Rose, Erivo and Robyns are starring in The Great British Musicals - in Concert, which plays three performances on 4 July and 5 July at the St James Theatre.