He studied violin with Józef Jarzębski at Warsaw Conservatory and with André Gertler at the Royal Conservatory of Brussels (1947–1948). Leader of Sopot Philharmonic Orchestra from 1945. From 1949 he taught at Warsaw’s State Higher School of Music, whose vice-chancellor he was in 1973–1975, and where he organised an Institute of Music Pedagogy. He also taught at the Indiana University School of Music in Bloomington (1965–1986).
Wroński gave performances throughout Europe as well as in Hong Kong, India, Iran, Japan, and the United States. He performed with orchestras, in a duo with Władysław Szpilman, with his own string quartet, and the Warsaw Quintet.