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 June 25, 1950. He served as a priest for two years (1950–1952) before returning to school, obtaining three doctorates by 1965 – one in theology from the Jagiellonian University, and Ph.D.s from the Lublin Catholic University and Warsaw Theological Academy. Appointed apostolic administrator of Lviv for territories within Poland in May 1984, he was consecrated bishop on June 23. He was made archbishop on January 16, 1991.