In 1937, he co-wrote (with Morrie Ryskind) the screenplay for Stage Door, starring Katharine Hepburn, Ginger Rogers and Adolphe Menjou.
This very loose adaptation of the play by George S. Kaufman and Edna Ferber was also nominated for the Academy Award for Best Picture.
Veiller was also Oscar-nominated for writing (with uncredited help from John Huston and Richard Brooks) The Killers (1946), an adaptation of the short story by Ernest Hemingway.
For State of the Union (1948), again directed by Capra, Veiller was credited as co-producer as well as co-writer.
Veiller worked with director John Huston on several films: Moulin Rouge (1952), Beat the Devil (1953), The List of Adrian Messenger (1963), and The Night of the Iguana (1964), the film of the Tennessee Williams play that became Veiller's final screen credit.