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. The club has also produced a number of other professional riders, including Richard Carapaz and Jonathan Caicedo.[6] Narváez became a multiple-time Pan American Junior champion in 2015.[7] For 2016, Narváez competed for Klein Constantia.[8]
Narváez started the 2017 season competing in the Volta ao Alentejo.[9] He won the Circuit des Ardennes with two stage runner-up finishes, despite a fall in the final stage.[10] He was the youngest winner of the event in a decade.[11]
In 2018, Narváez joined UCI WorldTeamQuick-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.[2]
He was named in the startlist for the 2019 Giro d'Italia.[13] He finished the race in 80th place. The following year he once again competed in the Giro; although he did not finish the race, he did win a stage; stage 12, which was an intermediate/hilly stage. Narváez finished just over a minute ahead of Mark Padun and nearly seven minutes ahead of 3rd place Simon Clarke.
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.
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