Graduate ofe the Kraków Music Academy in the classes of composition with Tadeusz Machl and Krzysztof Penderecki and conducting with Henryk Czyż and Krzysztof Missona. He perfected his skills at the Accademia Chigiana with Franco Ferrara. He is a laureate of leading national and international conducting competitions: 1st and 2nd conducting competition in Katowice (1st prize and the Music Critics' Prize), in Siena (1st prize) and Budapest (1st prize).
He conducts orchestras in Europe, Asia, Africa and both Americas, and collaborates with leading orchestras and operas in Poland. He has toured Europe with Polish orchestras. He has been among the conductors of numerous festivals, including: Warsaw Autumn, Poznań Spring, the Flanders Festival, Prague Jaro and Millenium Pace. While collaborating with Polish radio orchestras, he has made numerous archival recordings. He regularly sat on the Jury of the International Conducting Competitions in Katowice and Białystok and vocal competitions in Częstochowa.
Jerzy Salwarowski's discography includes many albums recorded for foreign labels: Amreco, Adda, Thorofon – and Polish labels: Tonpress, Selene, Wifon, DUX and Polskie Nagrania. For the latter he recorded an album with music by G. Gershwin, awarded the "Golden Record" in 1994, and released on CD in 1999. He made the first complete recording of Mieczysław Karłowicz's symphonic poems, released on CD and nominated for the "Fryderyk'99" award. Jerzy Salwarowski also recorded two CDs with the Toruń Chamber Orchestra and the first in the history of the Szczecin Philharmonic, the "Famous Caprices" album, which was nominated for the "Fryderyk'98" award. In the spring of 2002, together with his son Hubert, he recorded a CD featuring Johannes Brahms' Piano Concerto No. 1 in D minor, Op. 15 (accompanied by the NOSPR) and Sergei Prokofiev's Piano Concerto No. 3 in C major, Op. 26 (accompanied by the Szczecin Philharmonic Orchestra). This CD was nominated for the "Fryderyk 2002" award. In 2008, conducting the Warsaw Philharmonic Orchestra, he recorded a CD with Mieczysław Karłowicz's Symphony in E minor "Rebirth", Op. 7, which received excellent reviews.
He also conducts abroad: in Paris, Madrid, Barcelona, Prague, Bratislava, Hamburg, Cairo, Osaka, Skopje, Ljubljana, Porto, Luxembourg, Lucca, Everett (Washington), La Crosse (Wisconsin), Kiev, Berlin, Essen, Bergamo, Milan, Valencia and Copenhagen. In the spring of 2003 he gave guest lectures at Towson University Baltimore and Central Washington University in Ellensburg. Since 1999 he has lectured at the Academy of Music in Poznań, where he teaches conducting. In 2005, he received the title of professor from the President of the Republic of Poland. In 2008 he was appointed full professor. In June 2012, invited to the Naples Conservatory as part of the Erasmus program, he gave masterclasses there.
In 2011 he was awarded the Medal of the National Education Commission, and in 2013 he received the Gold Medal for Long Service and the Rector's Award. He regularly (every two years) leads concerts inaugurating the Academic Year with the university symphony orchestra. In 2005-2007 he was, for the second time, the Artistic Director of the Toruń Chamber Orchestra, later the Toruń Symphony Orchestra, with which he toured England in October 2006. From 2005 to 2011 he was the Artistic Director of the Częstochowa Philharmonic, with which he recorded the New Orleans Suite with the jazz band Five O'Clock Orchestra and a release in which the Częstochowa Philharmonic accompanied the jazz pianist Adam Makowicz (the album includes a piece dedicated to Częstochowa). In August 2008, invited by the National Orchestra of Rio de Janeiro.
In 2008, he was honored by the Minister of Culture and National Heritage Bogdan Zdrojewski with the Silver Medal for Merit to Culture Gloria Artis. His foreign performances in 2010 included both neighboring Ukraine (concert at the Philharmonic in Dnipropetrovsk) and exotic Jordan, in the capital of which he conducted the Łódź Philharmonic Orchestra during a concert at the end of the Chopin Year. The year 2011 brought another performance at the NOSPR, and concerts in Germany, and 2012 – concerts at the Poznań Spring, at the National Philharmonic, in Lviv and in Beirut. In May 2013, he conducted the Polish Radio Orchestra at the Warsaw Philharmonic, and in March last year he led the Sinfonia Juventus orchestra at the W. Lutosławski Studio in Warsaw. In 2014, he celebrated the 45th anniversary of his artistic work. On this occasion, he received the Award for lifetime artistic achievement from the Minister of Culture and National Heritage, Prof. Małgorzata Omilanowska. The anniversary was honored with a series of performances of the opera
Nabucco by G. Verdi in Poland and Germany with the Pro Musica Wrocław ensemble and many concerts in Polish orchestras.
In 2024 maestro Salwarowski is celebrating the 55th anniversary of his debut as conductor.