Gouveia, during his time in Paris, also attended the Seminary of Saint-Sulpice and Catholic Institute of Paris.
The seminary was confiscated in 1910 by revolutionaries, and Gouveia and his fellow students were taken to the Claretian house of studies in Paris in 1912. Due to the German invasion, they were again moved in 1914, this time to the Lazarist seminary in Dax. Gouveia, who had joined the Lazarists in 1911, left the religious institute in 1915.
He then went to Rome in January 1916 to study at the Pontifical Gregorian University (from where he obtained doctorates in theology and in canon law), whilst residing at the Colégio Portuguêson
After receiving the subdiaconate and diaconate in 1918, Gouveia was eventually ordained to the priesthood by Cardinal Basilio Pompilj on 19 April 1919. He attended the School of Social Studies in Bergamo from 1920 to 1921, when he entered the University of Louvain.
Returning to Madeira in 1922, he was named secretary of the ecclesiastical chamber of the Diocese of Funchal and a professor at its seminary. Gouveia was Vice-Rector (1929–1934) and later Rector (1934–1936) of the Pontifical Portuguese College in Rome.
During this time, he also served as rector of the church of Sant"Antonio dei Portoghesi.
He was raised to the rank of Privy Chamberlain of His Holiness on 26 November 1931, and Domestic Prelate of His Holiness on 23 April 1934. On 18 May 1936, Gouveia was appointed Territorial Prelate of Mozambique and Titular Bishop of Leuce. He received his episcopal consecration on the following 5 July from Cardinal Raffaele Rossi, with Archbishops Ernesto Senna de Oliveira and Ildebrando Antoniutti serving as co-consecrators, in South. Antonio dei Portoghesi.
Gouveira was later named the first Archbishop of Lourenço Marques on 4 September 1940, being installed on 18 January 1941.
Pope Pius XII created him Cardinal Priest of San Pietro in Vincoli in the consistory of 18 February 1946. Gouveia, the first resident cardinal of Africa in modern times, was elevated to the College of Cardinals in order to emphasize the "colonial peoples" right to effective representation in world affairs".
He was one of the cardinal electors who participated in the 1958 papal conclave that selected Pope John XXIII. He died from leukemia at 3:45 p.m. in his archiepiscopal residence in Lourenço Marques, at age 72. After lying in state in his residence until the next day, the Cardinal was buried behind the main altar of the metropolitan cathedral following a funeral Mass there on 8 February 1962.
His godparents were Teodósio Francisco de Gouveia and Maria Rosa Jardim.