The production opens at the West End's Vaudeville Theatre on 24 September 2014 (previews from 11 September) and runs until 22 November.
Rabbit Hole centres on Becca (Froggatt) and Howie Corbett, parents who have all that a family could wish for, until one day their world is suddenly turned upside down. Eight months following that life-shattering incident the young couple find themselves drifting perilously apart.
Rabbit Hole was first produced on Broadway in 2006. Cynthia Nixon (Sex and the City) played Becca, receiving the Tony Award for Best Actress in a Play for her performance. Lindsay-Abaire later adapted the play into a film starring Nicole Kidman.
Lindsay-Abaire's other plays include Good People, currently playing at the West End's Noel Coward Theatre starring Imelda Staunton.
Joanne Froggatt's previous stage work includes The Knowledge, Little Platoons (Bush Theatre), All About My Mother (Old Vic), Who's Afraid of Virginia Woolf? (Manchester Royal Exchange), Playhouse Creatures (West Yorkshire Playhouse) and Be My Baby (Soho Theatre).
Harman, who recently played Simon Cowell in I Can't Sing! at the Palladium, is also directing the UK tour of Shrek the Musical later this year, which he starred in in the West End, winning a WhatsOnStage Award.
Froggatt and Harman recently starred in one of Downton Abbey's most notorious plotlines, in which a butler, played by Harman, raped Froggatt's character Anna.
Of her casting in Rabbit Hole, Froggatt told the Daily Mail: "It's a part I've been waiting for ever to play. I totally fell in love with the play the moment I read it. It's heartbreaking, but really funny in parts as well. Becca's very different from Anna. She's American, and she's middle class, and she's going through this traumatic time over her child."