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.
Director Andrew Keates said: "In our current political climate, I can think of no better time to tell this visceral story of how we can learn from those that are different to us and also form lifelong relationships indiscriminate of age, gender and race."
Dessa Rose is produced by Arion Productions, whose previous productions include Passing By, As Is, Rooms - A Rock Romance and Howard Goodall's A Winter's Tale.
It runs at Trafalgar Studios 2 from 31 July to 30 August 2014 (previews from 29 July).