Some of his screenplays started as theater plays (for instance, Le dîner de cons). This theatrical experience contributes to his films' tight structure, resulting in what has been called "marvels of economy".
Many of his French comedies feature recurring types of characters, named François Pignon (a bungler) and François Perrin (a bully).
Veber was born in Neuilly-sur-Seine, Hauts-de-Seine, the son of a writer mother and Pierre-Gilles Veber, a screenwriter. Veber's father was Jewish and his mother was Armenian-Russian (Veber was baptized at birth). His grand-uncle was writer Tristan Bernard.
His parents were both authors: his father writer and journalist Pierre-Gilles Véber and his mother novelist Catherine Agadjanian, who wrote under the name Georgette Paul (1901-1990). He is the great-nephew of playwright, novelist, journalist and lawyer Tristan Bernard, grandson of playwright Pierre Véber and nephew of screenwriter, director and hit songwriter Serge Veber. He is the uncle of Sophie Audouin-Mamikonian, young adult author of the Tara Duncan series. His son, Jean Véber, is also a screenwriter.