Rev. Dr. Msgr. Alexander Baran was born on March 28, 1926 in Koncove, a suburb of Uzhhorod, Carpatho-Ukraine (then part of Czechoslovakia). His father, Viktor Barany, was a secretary to the Czechoslovakian prime minister, M. Hodzha (1935-1939). Rev. Baran obtained a B.A. (History-Slavic) at Charles University in Prague in 1948. He left Czechoslovakia after the Communist "putsch" in 1948 and continued his studies in Rome, Italy. In Rome he completed two doctoral degrees, one in theology (Urbanianum University) and one in history (Eastern Oriental Institute). During his years in Rome he studied and worked at the Vatican Archives. On March 25, 1954, he was ordained to the Ukrainian Catholic priesthood by Archbishop Ivan Buchko and worked as a priest among Ukrainian immigrants in England and Belgium.

In 1961 he arrived in Winnipeg where he worked in different parishes, such as Holy Eucharist, Blessed Virgin Mary, St. Josaphat, Christ the King and SS. Peter and Paul. In 1964 he became the chaplain of 'Obnova', the Ukrainian Catholic Students' organization at the University of Manitoba. In 1965 he started teaching at the University of Manitoba as a part-time lecturer. Rev. Baran became a full-time assistant professor (later associate professor) of history in 1966 and taught courses in East European history and Byzantine art history until 1991. He completed his studies in Canada when he received an M.A. (Slavic) from the University of Ottawa in 1976. Rev. Alexander Baran's main sphere of interest was Cossack history, Ukrainian Church history and Carpatho-Ukrainian (Ruthenian) history. He knew many languages including Ukrainian, English, Italian, Czech, Hungarian, and Latin. In 1968 Rev. Baran and George Gajecky spent time at the Viennese Archives going through 17th-century documents about the Ukrainian Cossacks' activities in western Europe. This research led to their two-volume work, The Cossacks in the Thirty Years War (1969, 1983). Another research project Rev. Alexander Baran was involved in was bringing the Vatican documents to Winnipeg relating to his project, "History of Roman Catholic Church in Canada from 1668". He acquired the documents for St. Paul's College and the documents were microfilmed in 1967 with grants from the Canada Council and National Archives of Canada.

Rev. Alexander Baran was the author of many scholarly works on the Church history of Carpatho-Ukraine (Ruthenia), on pre-Khmelnytsky Cossack history, and on Ukrainian church history in Canada. He published articles in the scholarly journals Alma Mater, Analecta OSBM, Logos, Bohoslovia, Harvard Ukrainian Studies, and Ukrainian Historian. He also published articles in the following volumes published by UVAN (Ukrainian Free Academy of Sciences in Canada): New Soil-Old Roots (1983), Millennium of Christianity in Ukraine 988-1988 (1989), and Jubilee Collection of the Ukrainian Free Academy of Sciences in Canada (1976). Rev. Baran also compiled and edited an unpublished manuscript about his father Viktor Barany titled Dennyk Viktora Barana (1996). In 1989 he collected research material in the Czech Archives for his book project, Statni Ustredni Archiv v Praze.
He passed away on March 12, 2004 in Winnipeg.