Mejía took up cycling at the age of 16, after watching Lucho Herrera, Fabio Parra and Óscar Vargas racing in the Vuelta a Colombia. He had previously competed in football and athletics, having been national junior champion for the 10,000 metres. In 1988 he won the Under-23 Vuelta a Colombia and the Clásico RCN. He won the young rider classification in the 1991 Tour de France and finished fourth at the 1991 UCI Road World Championships in Stuttgart, where he was part of the winning break alongside Gianni Bugno, Steven Rooks and Miguel Indurain. Mejía joined the Motorola team in 1993: that season he won the Volta a Catalunya and finished fourth in the 1993 Tour de France. Subsequently he spent two more seasons with Motorola before finishing his road racing career with the Petroleo de Colombia team. He spent two more years racing mountain bikes before retiring from competition. During his career he also won other stage races including the Vuelta a Murcia, Route du Sud and Vuelta a Galicia.