Directed by Ian Rickson (Jerusalem) and adapted by Duncan Macmillan (1984), the piece will run at the Duke of York's Theatre in the West End.
Burke, who recently appeared in the touring production of Don Carlos, will play Rosmer, a man haunted by history and living in a grand house owned by a powerful family. Atwell, whose credits include Measure for Measure at Donmar Warehouse and Dry Powder at Hampstead Theatre, will play Rebecca West, considered one of Ibsen's feminist heroines. The piece sees West try to undermine Rosmer's idealism and get him to understand a more free-thinking way of life on the eve of a major election.
The play first premiered in 1886, two years after Ibsen's The Wild Duck (which was recently revived at the Almeida). It was last seen in London in 2008, with Helen McCrory, Paul Hilton and Malcolm Sinclair leading the cast.
Rickson's production, produced by Sonia Friedman productions, will have set and costume design by Rae Smith, with lighting by Neil Austin, music by Stephen Warbeck, sound by Greg Clarke and casting by Amy Ball. Further casting is to be announced soon.
The piece runs from 2 May to 20 July, with previews from 24 April.