He was born to Rusyn immigrant parents in St. Clair, Pennsylvania and was educated in the public schools there.
He attended Illinois Benedictine College and St. Procopius Seminary, both in Lisle, Illinois, then was ordained to the priesthood on November 13, 1945 by Bishop Basil Takach at St. John the Baptist Byzantine Catholic Cathedral in Munhall, Pennsylvania.
Pope Paul VI conferred upon him the rank of Right Reverend Monsignor on October 25, 1963.
Thirty-two new parishes and missions were created during his tenure and two monasteries were established: the Basilian Fathers of Mariapoch in Matawan, New Jersey and the Byzantine Discalced Carmelites in Sugarloaf, Pennsylvania.
The Institute's library features a collection of rare Slavonic books and manuscripts.. Dudick also served as a member of the Congregation for the Oriental Churches and as a member of the Committee for the Revision of Eastern Canon Law.