Závada was born in to the family of a metal worker, his father died during the First World War, an event which left a huge impression on his future works.

Závada graduated from his doctorate in philosophy at the Charles University and started his literary career.

[1] Initially a representative of Poetism, he broke with the literary style in favor of a more gloomy and pessimistic romanticism.

After the invasion of Czechoslovakia by Nazi Germany, he became more reclusive and wrote Hradní věž, which was about his coming to terms with the fate of his country.

His son Jan Závada (1933–2024) was a Czech molecular oncologist, expert in virus genetics.