He was ordained June 11, 1932, the first native Utahan ordained for service in the diocese.  His first assignment was assistant pastor at the Cathedral, where he remained until August 1934.  Then he was posted to the College of St. Mary of the Wasatch as chaplain and instructor.

        He was editor of the Intermountain Catholic from July 1934 until September 1938, when he left to attend the Catholic University of America.  He received a degree of Doctor of Philosophy from there in 1941 with a major in American History.  He maintained an interest in history over the years, and after he became Archbishop he became a member of the board of advisors of the Western History Center at the University of Utah, and gave the second annual Lecture on the American West at the Hotel Utah.  This was sponsored by the University of Utah, the Utah State Historical Society, and the Association of  University Women.

        Upon his return to Salt Lake City in 1941, Father Dwyer was made editor of the paper, now named the Register, and became the Superintendent of Education of the Diocese.  In 1942, he became the director of the Propagation of the Faith, and in 1948 became Rector of the Cathedral.  He was appointed Bishop of Reno on August 5, 1952.  Bishop Dwyer's active life was interrupted on July 5, 1961,  by a severe heart attack.

        One of his pleasures was the writing of columns for his diocesan papers in Reno and in Portland, and other columns for various publications.  He had a real grounding in English and American literature and also was a student of the history of the Church.  He wrote articles from 1932 to 1938 and again from 1941 to 1976.   He maintained a group of loyal readers, and in his last illness received several hundred letters from people he had never met.

        Bishop Dwyer attended all of Vatican II.  He composed a number of columns about the Council, which gave an atmosphere of those days.  He voted in favor of most of the recommendations and changes.  He was one of the first to establish a priests' senate.  He brought the Reno Diocese into the newly organized Nevada Council of Churches, which was one of the first such councils in the country.

He was appointed Archbishop of Portland in Oregon on December 9, 1966.  He left the Reno Diocese in sound financial condition increasing the number of schools from five to nineteen, and building a high school at Reno.  The number of Catholics had increased over three times.

The new Archbishop was now entrusted with the care of a sizeable Catholic population in Western Oregon, and a number of churches, colleges, schools, and buildings for religious orders.  He had a steady, established body of the faithful, who had over the years demonstrated their loyalty to the Church and to their country.
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        Besides the problems attendant on administration of a large diocese, urgent problems soon appeared. The building of needed schools and other projects had required a bank debt of some $7 million.  Archbishop Dwyer undertook an extensive pledge program known as Action, which resulted in this debt being paid off.

        Finding his health slipping, he resigned on January 22, 1974.  At the installation of his successor, Archbishop Cornelius M. Power, Archbishop Dwyer was ill, and his address of welcome was read by Reverend Willis Whalen.  Soon afterwards he left for Piedmont, California, where he made a final home.  He interested himself in matters of art such as the Liturgical Arts Society.  He was chairman and editor of the National Catholic Register and was chairman of the Catholic Twin Circle.  During his last years, he wrote a series of lives in brief, about outstanding figures of the Church called The Saints Go Marching. His only published book was the historical study for his doctorate, The Gentile Comes to Utah, issued in 1941, and republished in 1971.  After his death a collection of his columns was issued under the title Ecclesiastes with the editorship of Albert J. Steiss (1982).

        Archbishop Dwyer died on the morning of March 24, 1976, in Piedmont, California. He was buried in Portland, and his funeral Mass took place at St. Mary's Cathedral.