Kaverin was born to the kapellmeister of the 96th Infantry Regiment out of Omsk, Abel Abramovich Zilber and his wife, Khana Girshevna Desson, who owned a chain of music stores.

[2] Kaverin studied at the Pskov Governorate Gymnasium and in 1923 graduated from the Leningrad Institute of Living Oriental Languages, specializing in Arabic.

Kaverin also married the younger sister of Yury Tynyanov, Lidia Nikolaevna, and had two children, Natalia and Nikolay.

During World War II evacuation in Yaroslavl, Kaverin completed his best-known novel, The Two Captains (1938–44), which colorfully recounts the adventures of Russian polar explorers before and after the Revolution.

As The Moscow News commented on his centenary, "Kaverin showed that even under the worst of conditions it is possible to retain one's human qualities and decency.