Born in Bohunhin, he was ordained to the priesthood on April 3, 1920. On October 5, 1939, Campbell was appointed Bishop of Argyll and the Isles by Pope Pius XII, receiving his episcopal consecration on the following December 14.
He was translated as Archbishop of Glasgow on January 6, 1945. In 1952, Campbell described Marshal Tito as a "modern Nero. He died at age 68.