He began his studies in 1857 at the Academia Imperial de Belas Artes (AIBA) under the direction of Victor Meirelles.

When he returned to Brazil in 1877, he temporarily replaced Meirelles as the Professor of history painting at AIBA; although his primary position was as a teacher of landscapes, nude figure painting and design at the Escola Nacional de Belas Artes (ENBA).

[2] Among his best-known students there were Rodolfo Amoedo, Henrique Bernardelli, Lucílio de Albuquerque and Giovanni Battista Castagneto.

In 1880, Emperor Pedro II (who was impressed by Costa's Italian education) commissioned him to paint murals in Candelária Church which, after a brief trip to Rome for inspiration, were done in collaboration with his students.

[2] He wrote a book, Mecanismos e proporções da figura humana (Mechanisms and Proportions of the Human Figure), which was published the year after his death and presents the essence of his artistic credo.