The Moscow-born poet published his first poems in 1958 and became one of the iconic artists of the Thaw, the brief era of liberalism ushered in by Soviet leader Nikita Khrushchev after the death of dictator Joseph Stalin.
In the 1960s, Voznesensky was one of several Soviet poets who gave poetry readings in stadiums and concert halls before huge crowds of transfixed listeners, sometimes numbering in the thousands.
He clashed with the authorities occasionally, most notably in a 1963 meeting between Khrushchev and artists where the Soviet leader personally threatened to exile him, shouting: "Take your passport and get out, Mr Voznesensky!"
Following Khrushchev's tirade, which reportedly gave the poet a nervous breakdown, Voznesensky walked a tightrope between defending his artistic integrity and refraining from offending the Soviet regime.
The authorities let him travel abroad and gave him the prestigious State Prize in 1978, but Voznesensky also contributed to the underground samizdat journal Metropol in 1979 in defiance of state censors.
Throughout his lifetime, Voznesensky published more than 20 collections of poetry and prose, as well as the libretto of the Soviet Union's first rock opera.
Russian President Dmitry Medvedev expressed his condolences to Voznesensky's family and friends, the Kremlin said in a statement.
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