The Gavin & Stacey actress will portray the titular character from Henrik Ibsen's classic 1890 play at London's Old Vic.
Kevin Spacey, artistic director at the theatre, said that he was "particularly pleased" with Smith's casting in "such an iconic and impactful play".
He said: "Sheridan is a wonderful actress who has rightly received acclaim for her recent work and I am sure audiences will be intrigued to see her tackle this role."
Brian Friel's adaptation of the play will open at the theatre on September 12.
It will be directed by Anna Mackmin, and will also star Doc Martin and Silk actress Buffy Davis.
Coronation Street star Anne Reid has also signed up to appear in the production.
Sheridan Smith previously won a Laurence Olivier Award for Legally Blonde: The Musical.
The actress is tipped to return for a Christmas episode of Jonathan Creek as sceptic Joey Ross.