Morais Cardoso was born in Murça, Portugal, the son of Hipólito de Morais Cardoso, Captain-Major of Murça, and wife Eufémia Joaquina. He was educated at the University of Coimbra, where he was awarded a licentiate in theology.
He was appointed as Bishop of Faro (or of Algarve) on 28 September 1863. He was consecrated on 14 February 1863 in Lisbon, by Cardinal Manuel Bento Rodrigues da Silva. He participated in the First Vatican Council that was called in Rome during 1869 to 1870. Morais Cardoso was promoted to the patriarchal see of Lisbon on 25 April 1871.