Zavadovsky was born Pokrovka-Skorichevo, Yelisavetgradsky Uyezd (now in Ukraine) in the landed family of Mikhail and Maria née Kotsiubinsky.
In 1919 he went with his students to Askania Nova in southern Ukraine and began to conduct experiments on gonadal transplantations in chickens to alter the sex of fowl.
In 1927 he was also in charge of the Moscow Zoo and was involved in studies to increase reproduction of farm animals using hormonal treatments.
In 1948 his department on developmental biology was closed and Zavadovsky was fired along with biologists like Nikolai Vavilov who were opposed to Trofim Lysenko.
A developmental laboratory was started again after Stalin's death and Zavadovsky worked there in his last years.