[4] Originally from El Playón de San Francisco, situated at an altitude of 2,990 meters, in Ecuador's Sucumbíos Canton,[5] whilst at school Narváez was a member of a cycling club founded by one of his teachers, former Olympic racing cyclist Juan Carlos Rosero.

[11] In 2018, Narváez joined UCI WorldTeam Quick-Step Floors on a three-year contract, making him one of only two Ecuadorians in the World Tour.

[12] In late 2018, Narváez broke his three-year contract with Quick-Step Floors to join Team Sky for the 2019 season.

In 2023, Narváez won the overall classification as well as three stages of the Tour of Austria, in addition to his second National Road Race Championship title.

[14] In May, he outsprinted Tadej Pogačar and Max Schachmann to win the opening stage of the Giro d'Italia, taking the maglia rosa in the process.