He was born on in Grand Rapids, Michigan, to Casimir, a Polish immigrant, and Mary Szoka. He did his primary studies at St. Michael School in Muskegon. He entered St. Joseph’s Seminary in Grand Rapids and then St. John’s in Plymouth, Michigan.

He was ordained a priest on June 5, 1954 in Marquette, Michigan and served as an assistant priest in the parish of St. Francis in Manistique, Michigan. In 1955, he became secretary to Bishop Noa of Marquette. During the period of 1955 and 1962, he also served as chaplain at St. Mary’s Hospital. In 1956, he was Roman Catholic chaplain at K. I. Sawyer, AFB, Michigan.

From 1957 to 1959, he attended the Faculty of canon law at the Pontifical Urban University in Rome. Upon returning to the United States, from 1960 until 1971 he served at the matrimonial tribunal of the diocese of Marquette, while at the same time serving as chancellor’s assistant (1962-69), and parish priest (1962-63) of St. Pius X parish in Ispheming on north Lake Superior, parish priest of St. Christopher’s (1963-71), then chancellor of the diocese of Marquette. He also accompanied Bishop Noa to the first session of the Second Vatican Council.

On June 11, 1971 he was elected Bishop of Gaylord, Michigan and was ordained on July 20, 1971. A year later, the Bishops of the 4th pastoral region of the National Conference of Catholic Bishops (NCCB) elected him president for the period of 1972-77. At the same time, he was treasurer and secretary of the Episcopal Conference of Michigan.

On March 21, 1981 he was named Archbishop of Detroit. Since 1981, he also served as president of the Administration Council of the provincial seminary of St. John in Plymouth, Michigan and Sts. Cyril and Methodius Seminary near Orchard Lake Village, Michigan. He was also a president of the board of directors of the Episcopal Conference of Michigan, member of the executive committee of the Catholic University, president of the Committee for University Relations, Administrator of the National Sanctuary of the Immaculate Conception, treasurer of the NCCB, and served on committees within the Conference for: human values, bishops, dioceses and provinces, and economic affairs.

He was created and proclaimed Cardinal by John Paul II in the consistory of June 28, 1988. His titular church is St. Andrew and St. Gregory at Monte Celio. He was President of the Prefecture of Economic Affairs of the Holy See, January 22, 1990 to October 14, 1997. He became Archbishop emeritus of Detroit, April 28 1990.

On October 14, 1997, Cardinal Szoka was named President of the Pontifical Commission for Vatican City State, and on February 22, 2001, President of the Governatorate of Vatican City State. Within the Roman Curia his membership is: Secretariat of State (second section), and Congregation for the Causes of Saints, Bishops, Evangelization of Peoples (Congregatio de Propaganda Fide), Clergy, Institutes of Consecrated Life and Societies of Apostolic Life (congregations).