Kushner was born in Leningrad into a Russian-Jewish family; his father was a naval engineer.

In 1965 he became a member of the Writers' Union, in 1987 joined the Russian PEN Center.

He is also editor-in-chief of Biblioteka poeta (the "Library of the Poet" series).

The Nobel Prize winner Brodsky once called Kushner "one of the best lyrical poets of the 20th century", adding that his name "is to stand in the line of names dear to the heart of every native Russian speaker"[2] Translations of Kushner's poetry into English, Italian and Dutch were published in book form; several poems were also translated to German, French, Japanese, Hebrew, Czech, and Bulgarian.

His numerous awards include the Russian National Award (1996) and the prestigious Pushkin Prize for poetry, bestowed on him by Russian president Vladimir Putin in 2001.