Born in Roberval, Quebec, the son of Georges Lévesque and Laura Richard, he was ordained into the priesthood in 1928. He studied philosophy and theology at the Dominican College in Ottawa and social sciences at the School of Social sciences of the Université Catholique de Lille. He was a professor at the faculty of Social sciences of Université de Montréal from 1935 until 1938 and a professor of social philosophy at Laval University from 1936 until 1962. In 1938, he founded the School of Social, Political and Economic Sciences of Laval University and was its first director from 1938 until 1943. The School became the Faculty of Social Sciences in 1943, and he was its first dean, from 1943 until 1955. He founded the Quebec Superior Council of Cooperation and was its first president, from 1939 until 1944. He founded the periodical Ensemble! and was its director, from 1939 until 1944. He was member of the Royal Commission on National Development in the Arts, Letters and Sciences in Canada. He was vice-president of the Canada Council for the Arts. He represented Canada at several international events. In 1963, he founded the National University of Rwanda and he was its first President, from 1963 until 1971. Lévesque supported the co-operative movement and, through his Faculty, helped create new social welfare bodies such as the Conseil supérieur de la coopération and the Société d'éducation des adultes, and to modernize Québec's church-controlled social welfare organizations. As well, his Faculty of Social Science trained a generation of union organizers. His liberal and social democratic ideas and work brought him into constant conflict with the government of PremierMaurice Duplessis and he is seen as one of the fathers of the Quiet Revolution that transformed Quebec society after Duplessis's death. In 1955, Prime Minister Louis St. Laurent approached Lévesque about naming him to the Senate of Canada as a non-partisan appointee. Lévesque agreed and the Dominican Order gave its permission but the appointment was vetoed by Archbishop Maurice Roy due to concerns that allowing a priest to accept a political appointment could potentially embarrass the Church.
