Furey was ordained to the priesthood by Cardinal Basilio Pompili on March 15, 1930.Following his return to Pennsylvania, he served as private secretary to Cardinal Dennis Dougherty. Furey was appointed in 1936 as president of Immaculata College in East Whiteland Township, Pennsylvania. He left Immaculata College in 1946 to become rector of St. Charles Borromeo Seminary. He was named a domestic prelate in 1947. In 1958, Furey left his position as rector to became pastor of St. Helena's Parish in Philadelphia.
