After studying at the seminary in Angra, Nunes went to Macau as a missionary on June 4, 1903, and was ordained to the priesthood on the following July 26. He then did pastoral work and taught at Macau's seminary until 1906. Nunes was named Vicar general of Macau and Timor from 1906 to 1913, when he began missionary work in Timor. He became Vicar capitular of Macau on February 21, 1917.
On December 16, 1920, Nunes was appointed Bishop of Macau by Pope Benedict XV. He received his episcopal consecration on November 20, 1921, from Bishop Emanuel da Costa, with Bishops Manuel Augusto Xavier and Francisco Nunes da Rocha serving as co-consecrators. Nunes was advanced to the Archdiocese of Goa e Damão, with title of Patriarch of the East Indies, on December 11, 1940. Resigning as Archbishop on December 16, 1953, he was made Titular Archbishop of Odessus and Vice-Camerlengo of the Holy Roman Church that same day, whilst retaining the personal title of "Patriarch".
Pope John XXIII created him Cardinal Priest of S. Prisca in the consistory of March 19, 1962. Nunes attended the Second Vatican Council from 1962 to 1965, and was one of the cardinal electors who participated in the 1963 papal conclave that selected Pope Paul VI. He served as the papal legate to the fourth centennial celebration of the arrival of the first Catholic missionaries to Macau on November 10, 1965.
The Cardinal died in Rome, at age 96. He was initially buried in the Campo di Verano cemetery, but his remains, in accord with his will, were later transferred to the church of S. Antonio dei Portoghesi. In his will, Nunes also expressed his desire to be buried in the cemetery of Horta, next to his parents, if he died in Portugal.