Father Robert Joseph Welsh was born in Philadelphia, Pennsylvania, to Robert Welsh and Elizabeth Walpole on 15 July 1921. He had one brother and four sisters. Baptized in the church of Saint Agatha in Philadelphia on 7 August 1921, he began his education in that parish. After finishing grammar school he attended West Catholic High School in Philadelphia, from which he graduated in 1938. After a semester at La Salle College in Philadelphia, he transferred to Augustinian Academy, the Preparatory Seminary on Staten Island, New York, as a post-graduate student. In September 1939, he was received as a novice and spent a year at Our Mother of Good Counsel Novitiate, where on 10 September 1940, he professed simple vows. Three years later, at Saint Mary's Hall, the Augustinian collegiate seminary on the Campus of Villanova College in Pennsylvania, he professed solemn vows. He graduated from Villanova in 1943 with an A.B. degree and began his study of theology at Augustinian College in Washington, D.C. During the summer months he took graduate courses in English at the nearby Catholic University of America. On 11 February 1947 he was ordained to the priesthood at the National Shrine of the Immaculate Conception in Washington, D.C. Following ordination, he was sent to Collegio Santa Monica, the Augustinian international house of studies in Rome, Italy. There he began graduate studies in theology at the Gregorian University. In 1948 he earned an S.T.L., degree and two years later was awarded an S.T.D. cum laude.
Father Welsh's first assignment was to Augustinian College in Washington, D.C., where from 1950-1956 he taught moral theology and was Submaster of Professed. In 1956 he was transferred to Villanova University, where he taught in the department of theology until 1965. From 1956 to 1959 he also served as Secretary of the Province of Saint Thomas of Villanova. In 1960 he was appointed Assistant Dean of Liberal Arts and Sciences, and the following year became Dean. In 1967 Father Welsh became the 28th President of Villanova University, a position he held until 1971. These were years of change and campus unrest during which his patience and understanding was greatly appreciated by both students and faculty. In 1971 he was named prior of Augustinian College in Washington, D.C., and was chosen to serve at the same time as President of the Washington Theological Union. In 1975 he was elected to the Council of the Province of Saint Thomas of Villanova and was transferred to Saint Thomas of Villanova Monastery, Villanova, Pennsylvania. On the Council Father Welsh served as Province Director of Education until 1979. From 1980 to 1984 he brought his wealth of experience to Malvern Preparatory School, Malvern, Pennsylvania, becoming there a popular and respected guidance counselor. In 1985 Father Welsh was named treasurer of the Province of Saint Thomas of Villanova and held that position until 1988. In that year he was named Assistant to the President of Villanova University, a position he continued to hold even as his health began to fail. During his active years in the education apostolate, Father Welsh served on the Boards of Trustees of Villanova University, of Merrimack College in North Andover, Massachusetts, and of Malvern Preparatory School, Malvern, Pennsylvania. A building on the West Campus of Villanova University has been named in his honor.
A very private person, Father endured with patience the discomfort associated with the treatment of his final illness giving all with whom he was associated an example of Christian suffering. At his death Father Welsh was survived by two sisters, one of whom was an invalid, whom he had continued to visit even as his own health failed.
A Mass of Christian Burial was celebrated at Saint Thomas of Villanova Church on 11 November 1992. Father Edmund J. Dobbin, O.S.A., then President of Villanova University, delivered the homily. The following day the interment took place in the Augustinian plot of Calvary Cemetery in West Conshohocken, Pennsylvania.