Born as son of Wincenty and Stanisława Łastowiecka in Lwów, Poland (now Lviv, Ukraine), Jaworski studied at the Lwów Major Seminary and was ordained in Kraków on 25 June 1950.
Lahir sebagai putra dari pasangan Wincenty dan Stanisława Łastowiecka di Lwów, Polandia (sekarang Lviv, Ukraina), Jaworski belajar di Seminari Besar Lwów dan ditahbiskan di Kraków pada 25 Juni 1950.