He was born in Cracow, where he graduated with honours from the Academy of Music - composition under Tadeusz Machl and Krzysztof Penderecki, conducting under Henryk Czyż and Krzysztof Missona. He perfected his conducting skills at the Accademia Chigiana in Siena under Franco Ferrara. He has won in both national and international competitions: the 1st and 2nd Conducting Competition in Katowice - the Music Critics' Prize and Second Prize, International Conductors' Competition in Siena - First Prize; Iternational Conductors' Competition in Budapest - Second Prize (first one not awarded).
He conducted chamber and symphony orchestras, as well as opera performances across Europe, Asia, Africa and North America.
Jerzy Salwarowski has given numerous performances abroad, including such places as Hamburg, Cairo, Osaka, Skopje, Porto, Luxembourg, Lucca, Everett (Washington), La Crosse (Wisconsin), Kiev, Berlin, Essen, Bergamo, Milan, Barcelona, Valencia and Copenhagen.
In the spring of 2003, he gave lectures and masterclasses at the Towson University of Baltimore (MA) and Central Washington University of Ellensburg (WA).
Since 2000, he has been teaching at the Music Academy in Poznań. He was appointed professor by the President of Poland in 2005, and promoted to Full Professor in 2008.
Between 2005 and 2007 Salwarowski once again took the position of the Director of the Toruń Chamber Orchestra (which later became the Toruń Symphony Orchestra), and made a tour of England accompanied by it in the October of 2006.

In the years 2005-2011 he was Artistic Director of the Częstochowa Philharmonic.
During that time, a CD has been recorded in cooperation with the Five o'clock jazz orchestra, containing the New Orleans Suite, as well as another release, where the Philharmonic's musicians accompanied jazz pianist Adam Makowicz.