Sergei Klimenko was born in 1974 in Moscow. In 1998, he graduated from the M.M. Ippolitov-Ivanov State Musical Pedagogical Institute (Associate Professor Alexander Solovyev's classes}.
He started his professional activity in 1994, having worked in the Moscow State Symphony Orchestra, the A.V.Alexandrov Academic Song and Dance Ensemble of the Russian Army, the Moscow State Academic Symphony Orchestra directed by Pavel Kogan. Since 2003, he has been an artist of the National Philharmonic Orchestra of Russia.
He is an awardee of the International Woodwinds and Percussion Instruments Competition after N.A.Rimsky-Korsakov (2005, 3rd Prize) in Saint Petersburg.
He has performed with chamber ensembles and as a soloist in Russia, France, and the US, taken part in the Retrieval chamber music festivals (as a member of the NPR's Brass Quintet), the Nights in Mariinsky, the Skobelev Festival, the All-Russia Trombonists Seminar, Russian orchestral-choral assemblies, “The Christmas Festival at the Gnessins” and others. A participant of the Quartet 4x4 at the Culture TV channel (2019).