Born of a Jewish mother and a Protestant father, in Berlin, Germany, he came to Canada from England as a war refugee. He arrived by boat in Quebec in 1940 with other Germans, most of them Jewish, and they were interned in refugee camps, under military control. After some transfers between Quebec, Trois-Rivières, New-Brunswick and Farnham, he was finally interned to Sherbrooke. Being only 17 years old at this time, he considers this period of his life as an incredible adventure. Among the refugees, some intellectuals hastened to set up inside the camps educational systems of which he took advantage. Although Canada had no law for the refugees at this time, a lady who met them in these camps, put pressure on the government so that some of them could complete their studies outside of camps with financial aid that she had collected for scholarships.
He received a Bachelor of Arts degree in mathematics and physics in 1946 from McMaster University, a Master of Arts degree in mathematics in 1947 from Ohio State University, and a Th.D. in 1956 from the University of Fribourg.
He was the Professor of theology and sociology at University of Saint Michael's College in the University of Toronto and subsequently professor of theological ethics at McGill University's Faculty of Religious Studies. He is currently associated with the Jesuit Centre justice et foi in Montreal.
During the church council Vatican II he was a peritus, or theological advisor, at the Ecumenical Secretariat, the commission responsible for three conciliar documents, On Religious Liberty, On Ecumenism, and On the Church's Relation to Non-Christian Religions.
In particular, he advocated the position, as a response to the Holocaust, of the rabbi and philosopher Emil Fackenheim regarding the cessation of efforts to convert the Jews, famously stating: "After Auschwitz the Christian churches no longer wish to convert the Jews. While they may not be sure of the theological grounds that dispense them from this mission, the churches have become aware that asking the Jews to become Christians is a spiritual way of blotting them out of existence and thus only reinforces the effects of the Holocaust."
From 1962 to 2004, he was the editor of The Ecumenist, a review of theology, culture and society, as well as a member and frequent editor of the international Catholic review Concilium.
His books include:
- That They May Be One, Newman Press, 1958.
- The Future of Belief Debate (ed.), Herder & Herder, 1967.
- The Credibility of the Church Today, Herder & Herder, 1968.
- Man Becoming, Herder & Herder, 1970.
- Religion and Alienation, Paulist Press, 1975.
- Truth Beyond Relativity: Karl Mannheim's Sociology of Knowledge, The Marquette Lecture, Marquette University Press, 1977.
- The Priority of Labour: Commentary on John Paul II’s `Laborem exercens,’ Paulist Press, 1982.
- Theology and Society, Paulist Press, 1986.
- Compassion and Solidarity: The Church for Others (The 1987 CBC Massey Lectures), Anansi Press, 1988.
- The Church in Quebec, Novalis, 1992.
- Karl Polanyi on Ethics and Economics, McGill-Queen's University Press, 1996.
- Nationalism, Religion and Ethics, McGill-Queen's University Press, 2001.
- Signs of the Times: Religious Pluralism and Economic Injustice, Novalis, 2008.
- The Theology of Tariq Ramadan: A Catholic Perspective, University of Notre Dame Press, 2009.
A second edition of his seminal 1975 book, Religion and Alienation was republished by Novalis in 2006.
He holds honorary doctorates from Huron University College, London, Ontario; St. Francis Xavier University, Antigonish, N.S; Ohio Wesleyan University, Delaware, Ohio; Lafayette College, Easton, Pa.; Waterloo Lutheran University, Waterloo, Ontario; McMaster University, Hamilton, Ontario; Concordia University, Montreal.
Baum left the priesthood through automatic excommunication when he married without dispensation from his vow of celibacy in 1976. In 2012 he signed the Catholic Scholars' Jubilee Declaration on reform of authority in the Catholic Church. 
- Ed. Gregory Baum, The Twentieth Century. A Theological Overview, (Orbis Books Maryknoll, New York - G. Chapman, London 1999), cited in Ucko, Hans. "Towards an Ethical Code of Conduct for Religious Conversions".
- "Order of Canada citation".
- "Gregory Baum".
- An Interview with Gregory Baum “Faith, Community & Liberation”
- Concordia University Honorary Degree Citation, November 2002, Concordia University Records Maanagement and Archives