He served as Bishop of Sioux Falls from 1896 until his death in 1921. In 1853 he and John Ireland were chosen by Bishop Joseph Crétin to study for the priesthood in France. Upon his return to Minnesota, O'Gorman was ordained a priest on November 5, 1865.
He returned to Minnesota in 1882 and was then appointed pastor of Immaculate Conception Church at Faribault. In 1885 he became the first president of the newly established College of St. Thomas, where he also served as professor of dogmatic theology. He was named professor of church history at Catholic University of America in Washington, D.C. in 1890.
On January 24, 1896, O'Gorman was appointed the second Bishop of Sioux Falls, South Dakota, by Pope Leo XIII. He was later installed at Sioux Falls on May 1, 1896. During his 25-year-long tenure, he increased the number of priests and Catholics in the diocese, and erected numerous churches, schools, and hospitals. He dedicated St. Joseph's Cathedral in 1919, and founded Columbus College in 1921.
O'Gorman later died at age 78. O'Gorman Catholic High School in Sioux Falls is named in his honor.