[1][3] Having started shooting at the age of fifteen, Velarte served most of his sporting career as a full-time member of the La Rioja Shooting Federation (Spanish: Tiro Federal La Rioja) in his native Buenos Aires under head coaches Julio Escalante and Ariel Martínez.

[5][6][7] Despite missing out his 2000 Olympic bid, Velarte reached the peak of his shooting career by claiming the first gold medal for Argentina in the men's air rifle at the 2003 Pan American Games in Santo Domingo, Dominican Republic with a total score of 692.5 points.

Because of his remarkable victory, Velarte had guaranteed a place on the Argentine team and attained a mandatory minimum score to compete for the Olympics, signifying his return from an eight-year absence.

[8] In the 10 m air rifle, Velarte shot 586 out of 600 to finish in a two-way tie with Serbia and Montenegro's Stevan Pletikosić for thirty-ninth place.

[10] Four days later, in the 50 m rifle prone, Velarte scored 584 points to grab the penultimate position in a field of forty-six shooters, betraying a three-point gap from Cuba's Reinier Estpinan in the prelims.