She joins a cast that includes Natascha McElhone in the bunny boiler role made famous by Glenn Close in the 1987 film about a casual fling that goes wrong when Close's character becomes obsessed with lawyer Dan Gallagher and his family.
Mark Bazeley will play Gallagher, the role played by Michael Douglas in the film, with Davis as his wife.
Davis played Charlotte in Sex and the City for more than five years and also appeared alongside co-stars including Sarah Jessica Parker and Kim Cattrall in two film versions of the show.
Close was nominated for an Oscar for her role as the obsessive other woman who in one scene famously cooks a pet rabbit belonging to her ex-lover's family.
The play, directed by Trevor Nunn, opens at the Theatre Royal Haymarket on March 25