Narváez was the son of a cabinetmaker and restorer. While he was still very young, the family moved to Caracas and he began his studies at the Academy of Fine Arts. In 1928, he left for Paris where he attended the Académie Julian and established connections with the artistic community in Montparnasse. He returned to Venezuela in 1931 and, a few years later, began to work with the architect Carlos Raúl Villanueva, who commissioned him to supply sculptures for his projects, including the Plaza of Carabobo Park, the facade for the Museum of Fine Arts, the Museum of Natural Sciences and the Plaza O'Leary.
In 1939, he traveled to New York to decorate the Venezuelan pavilion at the World's Fair and exhibited his works "Café y Frutas" (now in the Andrés Bello Lyceum) and "Perlas y Cacao" (now in the Fermín Toro Lyceum).
In 1952, he completed an equestrian statue of General Rafael Urdaneta which is now on display in the Plaza La Candelaria. Later, he collaborated with Villanueva to create several pieces for the University City of Caracas, which was conceived as a "synthesis of the Arts". "Education", "Science", "The Athlete" and the bust of José María Vargas are some of his works located on the campus of the Central University of Venezuela.
In 1981 and 1982, he created two sculptures of monumental proportions. One of them, "Gran Volumen", was made for the Amuay Refinery Complex and the other, one of his last completed works, the "Armonía de Volúmenes y Espacio", was for Caracas Metro. It is located in a plaza that was later named for him.