The five-part miniseries is set during World War I and is based on the 1920s four-book series by British writer Ford Madox Ford.
Susanna White will direct the miniseries that centers on a love triangle between a conservative English aristocrat (Cumberbatch), his mean socialite wife (Hall) and a young suffragette.
Selwyn Roberts and David Parfit will produce the miniseries. Production begins this fall.
Stoppard has written several Tony Award-winning plays including Rosencrantz and Guildenstern Are Dead, Travesties, The Real Thing and The Coast of Utopia trilogy. He is also the author of Arcadia, currently running on Broadway through June 19 at the Ethel Barrymore Theatre. He won an Academy Award for his screenplay "Shakespeare in Love."
Hall has performed in West End productions including Mrs. Warren's Profession, As You Like It, The Cherry Orchard and Twelfth Night. Cumberbatch, who recently alternated the roles of Victor Frankenstein and the Creature in Frankenstein at National's Olivier Theatre, has also been seen in the West End in After the Dance and Hedda Gabler. He is the star of the TV series "Sherlock," playing the title detective.