Smirnov was born in Minsk[1] into a family of opera singers: his parents were Nikolay Senkin-Sadovsky and Eugenia Smirnova.

[2] He studied at the Moscow Conservatory from 1967 to 1972,[2] composition with Nikolai Sidelnikov, instrumentation with Yuri Kholopov, and analysis with Edison Denisov.

[1] His two operas Tiriel and Thel on text by William Blake were premiered in 1989, the first at the Freiburg Festival in Germany, and the second at the Almeida Theatre in London.

[4] His work has been performed by many notable conductors, including: Riccardo Muti, Sir Andrew Davis, Dennis Russell Davies, Peter Eötvös, Oliver Knussen, Vassily Sinaisky, Pavel Kogan, Gennady Rozhdestvensky, Gunther Schuller, and Yan Pascal Tortelier.

[3][5] Smirnov's works were published by Hans Sikorski in Hamburg,[3] Boosey & Hawkes in London,[1][6] and G. Schirmer in New York City.