Lansbury, 88, will play Madame Arcati, a clairvoyant who summons spirits of the dead. She won her fifth Tony Award for playing the role in a 2009 Broadway staging.
The BBC said this will be Lansbury's first appearance on the London stage in almost 40 years. She last starred in the 1974 production of "Gypsy."
Preview performances of "Blithe Spirit" are to begin March 1.