Born in Athens in 1972, Currentzis studied piano and violin as a child. A prodigy, he entered Greece's National Conservatory at 12, as a violinist, switching to composition several years later. In the 1994 he moved to Russia and began studying conducting with the nonagenarian Ilya Musin at the State Conservatory in St. Petersburg, graduating in 1998. He pointed out that with Greece's long history of military dictatorship, including the one in force when he was born, a move to Russia was in no way surprising, and indeed he has become an icon of intellectual freedom in the music sphere among progressive forces in his adopted country. He is a naturalized Russian citizen.
In 2004, while he held the position of music director of the Novosibirsk State Opera and Orchestra, Currentzis founded and became artistic director of MusicAeterna, leading both the choir and ensemble in period-style performances. In 2006, he also started the Territoria Modern Art Festival in Moscow. Remaining in Novosibirsk until 2010, Currentzis became the artistic director of the Perm State Opera and Ballet Theater. He was the recipient of the Golden Mask theatrical award, and he received awards for his performances of Henry Purcell's The Indian Queen, Alban Berg's Wozzeck, Sergey Prokofiev's Cinderella, and Wolfgang Amadeus Mozart's Le nozze de Figaro. Currentzis remains director of MusicAeterna and has toured Europe with new productions of Purcell's The Indian Queen and other Baroque operas. He made several recordings of the Alpha label, beginning in 2008, and including one of the Shostakovich Symphony No. 14, Op. 135, one of his few non-operatic releases. But it is his approach to Mozart that has made headlines and attracted the attention of the multinational Sony label. With blistering tempi, furious attacks influenced by his historical Baroque performance background, and an international group of singers handpicked to keep up with him, Currentzis' cycle of Mozart operas (Don Giovanni was recorded in Perm in 2016) has excited, and to an extent polarized, critics and listeners. Currentzis, who reportedly changes romantic partners annually like some do their automobiles, has stated that he is happy in Perm, in the Ural mountains, and has no plans to leave.