Farrow will make her first appearance on the Great White Way in nine years in September (14), when she will feature opposite Brian Dennehy in the two-person show, about letters exchanged over the years between two childhood friends.
She will depart on 10 October (14) to make way for Burnett, who will co-star with Dennehy until 7 November (14).
The changing monthly line-up will continue with M*A*S*H star Alan Alda and Murphy Brown's Candice Bergen, before Stacy Keach and Diana Rigg take over in early December (14).
The production will close on 1 February (14) with Martin Sheen and Huston playing respective characters Andrew Makepeace Ladd Iii and Melissa Gardner.
Gregory Mosher will direct the Pulitzer Prize-nominated play at the Nederlander Theatre.
Love Letters originally debuted on Broadway in 1989 with Colleen Dewhurst and Jason Robards.