Roger Michell (Some Americans Abroad) will direct the play, which follows a politician embroiled in a scandal after his affair with a married woman ends in a botched abortion and death.
The play, which was first written in 1907, was not performed until 1936 due to being banned by the Lord Chamberlain.
West is currently starring in the TV drama "The Affair." He recently appeared in the historical drama "Pride," as well as the TV series "The Hour" and "The Wire." He performed on Broadway in 2001 in Design for Living.