After completing his philosophical and theological studies at the seminary in Pinsk, Świątek was ordained as a Roman Catholic priest in 1939, and then was sent to the parish of Pruzhany.

Father Świątek escaped from prison, taking advantage of the confusion caused by the Nazi German invasion of the Soviet Union on 22 June 1941, and returned to Pruzhany.

[2] In 1988, he was made a Monsignor by Pope John Paul II, who in 1991 appointed him Metropolitan Archbishop of Minsk-Mohilev and Apostolic Administrator of Pinsk, and on 26 November 1994 created him Cardinal-Priest of San Gerardo Maiella.

"[2] In July 2006, Świątek, then aged 91, his resignation for reasons of age and declining health from the offices of Metropolitan Archbishop of Minsk-Mohilev was accepted by Pope Benedict XVI, but he remained Apostolic Administrator of Pinsk until 30 June 2011, when Tadeusz Kondrusiewicz, his successor as Metropolitan Archbishop of Minsk-Mohilev, replaced him also as Apostolic Administrator of Pinsk.

Pope Benedict XVI sent a telegram to Archbishop Kondrusiewicz and the Conference of Catholic Bishops of Belarus expressing his condolences for the Cardinal's death and praising him for his lengthy service as Cardinal Archbishop and his continuing fidelity and loyalty to the Church and to Christ during his periods of imprisonment back in the early years of the Cold War, in the post-war period, when the Church in the Soviet Union had to be largely clandestine.