McCann was born in Woodstock in Cape of Good Hope, and studied at Saint Joseph College in Rondebosch, University of Cape Town, and Pontifical Urbaniana University in Rome. He was ordained to the priesthood on 21 December 1935. In 1941, he became editor of The Southern Cross, South Africa's national Catholic newspaper, and held this post until 1948; he again became editor in 1986, this time for a five-year period. He did pastoral work in Cape Town from 1948 to 1950.
On 12 March 1950, McCann was appointed Apostolic Vicar of Cape Town and Titular Bishop of Stectorium. He received his episcopal consecration on the following 18 May from Archbishop Martin Lucas, SVD, nuncio to South Africa. Upon Cape Town's elevation to a diocese on 11 January 1951, McCann was appointed Archbishop of Cape Town, the first of metropolitan rank. Between 1961 and 1974, he served as President of the Southern African Catholic Bishops Conference (SACBC). McCann attended the Second Vatican Council, at which he was elected to the Commission for Bishops and made four written and four oral submissions in his own name and five written ones as president of the SACBC.
McCann was created Cardinal Priest of Santa Prassede by Pope Paul VI in the consistory of 22 February 1965, becoming the first South African to receive the red hat. He was one of the cardinal electors who participated in the August 1978 papal conclave, which selected Pope John Paul I, and the October 1978 papal conclave, which selected Pope John Paul II. McCann was reportedly a supporter of Giovanni Benelli at the latter conclave, but still gave his praise to the newly elected Wojtyla. Cardinal McCann retired as Archbishop of Cape Town on 20 October 1984.
He died on 26 March 1994, at age 86, and is buried in the archdiocesan cathedral. President Nelson Mandela, in an official condolence statement on the following 28 March, described Cardinal McCann as "one of South Africa's great sons" and "a man of great ability and wisdom".
- The Southern Cross. Inside the conclave of October 1978 October 1978
- African National Congress. Condolences with the Death of Owen Cardinal McCann 28 March 1994