Set in New York, the play tells the story of a novelist on the brink of success while his wife struggles with addiction and mental illness.
Double Oscar-nominee Malkovich has already directed versions of the play in Paris and Mexico City.
This English-language production marks his London directorial debut.
Malkovich said: "I'm delighted to be working at the Rose and very pleased to be working again on the Good Canary, and to be finally working on the play in its native language."
Malkovich's theatre work includes True West, Death of a Salesman and Burn This. He worked on more than 50 Steppenwolf Theatre Company productions in Chicago in the 1970s-80s.
His film credits include Being John Malkovich, Burn After Reading, Dangerous Liaisons, The Portrait of a Lady, Places in the Heart, In The Line of Fire, Of Mice and Men, The Sheltering Sky  and Empire of the Sun.
Playwright Helm's work in Hollywood includes screenplays for Stranger Than Fiction and Mr Magorium's Wonder Emporium (which he also directed).
Earlier in the Rose's season, Trevor Nunn will direct King John following his 2015 production of The Wars of the Roses. The production in May is the penultimate play in Sir Trevor's undertaking to direct all of Shakespeare's plays.
Arthur Miller's classic All My Sons, directed by Michael Rudman, will also begin previews in October.
John Malkovich is to direct the UK premiere of Zach Helm's play Good Canary at the Rose Theatre, Kingston, this autumn.