There are no dates currently set for the production, which is directed by British dramatist David Hare, but speaking at a press briefing for the National's annual report, Hytner said the play will arrive in the spring.
Joan Didion's The Year of Magical Thinking is based on the author's best-selling memoir. The one-woman show received its world premiere at Broadway's Booth Theatre, opening on March 29.
The play recounts the traumatic events that surrounded the death of Didion's husband, writer John Gregory Dunne, and their daughter Quintana, who was in a coma at the time of Dunne's death.
The National's 2008 season will also feature a complete reworking of Ibsen's Little Eyolf, directed by Marianne Elliott; a new play by poet Tony Harrison about the classicist Gilbert Murray (1866–1957); and a new work by Michael Frayn, to be directed by Michael Blakemore.
Hytner also confirmed that the National will next year stage a new "very big play" by Hare, to be directed by Howard Davies.
The productions will join Ralph Fiennes' previously announced return to the National in a revival of Oedipus, directed by Jonathan Kent.
For more on the National's current season visit www.nationaltheatre.org.uk.