The production, a remounting of last year's Theatre Royal Bath revival, runs at Hampstead from 12 September to 12 October 2013 (previews from 5 September).
The play imagines the fall-out when two of the 20th century's most brilliant and original minds - Sigmund Freud (Sher) and Salvador Dalí (Schiller) - collide in Swiss Cottage in 1938.
David Horovitch's many credits include roles in Grief (National Theatre), When We Are Married and Absurd Person Singular (Garrick), Bedroom Farce (Duke of York's), Life Is A Dream and Mary Stuart (Donmar Warehouse).
Adrian Schiller's previous theatre appearances include in The Veil and Every Good Boy Deserves Favour (National Theatre), Our Private Lives (Royal Court) and playing Ian Dury in Hit Me! The Life and Rhymes of Ian Dury (Leicester Square Theatre).
Lydia Wilson's previous roles include ‘Tis Pity She's A Whore (Cheek By Jowl) Acid Test and The Heretic (Royal Court), Blasted (Lyric Theatre, Hammersmith) and Pains Of Youth (National Theatre).
Hampstead artistic director Edward Hall said: "We are delighted to welcome Terry Johnson back to Hampstead this autumn. His longstanding relationship with Hampstead has continued over the last twelve months with his productions of Old Money and Race, and now he will direct his brilliant Hysteria."