Sophie Thompson is to play Lady Bracknell alongside Jeremy Swift as Reverend Chasuble and Sinead Matthews as Gwendolyn Fairfax.
Directed by Michael Fentiman, The Importance of Being Earnest is the final in the cycle of Wilde's plays programmed by Dromgoole. Other shows in the season were De Profundis, An Ideal Husband, A Woman of No Importance and Lady Windermere's Fan, with actors including Eve Best, Samantha Spiro, Joseph Marcell Simon Callow and Jennifer Saunders starring.
Dromgoole said: "It has been an enormous pleasure over the last nine months to showcase Oscar Wilde's dazzling ability to allow contraries free play in the world of his drama, and to highlight his take-down of puritanism and his love of mercy."
The Importance of Being Earnest runs between 20 July and 20 October and ends the programme, which has been seen by over 120,000 people in the Vaudeville.