Narvaja was born on March 17, 1819 in Córdoba, Argentina, to father Pedro Narvaja Dávila and mother Mercedes Montelles. He attended school in his hometown Colegio de los Franciscanos and later in Buenos Aires, where he received his doctorate in theology and jurisprudence. At the end of 1840 Narvaja arrived in Montevideo, renewed his title as a Doctor of Jurisprudence and was received as a lawyer. Shortly after the Sitio Grande during the Uruguayan Civil War he returned to Buenos Aires, and later traveled to Bolivia in the Argentine Andean Provinces located in Chile until the end of 1843. Upon his return to Montevideo he practiced as a lawyer, and published legal works and in 1855 he was admitted to the Facultad de Jurisprudencia as a professor of Civil Rights, a chair that he held until 1872, year in which the Tribunal Superior de Justicia was integrated. In 1875, he was elected the deputy for Durazno. This same year he was designated as the Minister of the Government, a position he maintained until February 1876, when the military epoch under PresidentLorenzo Latorre began. Narvaja drafted the Código Civil de Uruguay, a work of exemplary merit which was put into effect in 1868; he was the author of the Código de Minería which became valid on January 17, 1876. He also contributed substantially to the correction of the Código de Comercio that had been prepared by Dr. Eduardo Acevedo Díaz. Later on, he drafted numerous works and laws, as well as being a decisive and effecter impeller of the legislation that gave Uruguay the ability to consolidate as an independent state. In 1854 he married Joaquina Requena Sierra with whom he had a daughter named Mercedes. After her death in 1865, he remarried with Umbelina Tapia y Sierra with whom they had five children: Manuel Tomás, Tristán Hilario, Alfredo, Ricardo T., and Augusto. Narvaja died on February 19, 1877 in Montevideo, after a brief illness. He published, among others, as an author the following works:
A street in the Cordón neighborhood of Montevideo is named after him, equally famous is the street market which also bears his name, held every Sunday.