Vélez Trujillo was born on June 17, 1943, in Medellín, Antioquia where he also attended primary and secondary school in the Colegio de San Ignacio.
He moved to Bogotá to study at the Pontifical Xavierian University where he graduated with a Doctorate in Law and Economics.
He was appointed Ambassador of Colombia to the Kingdom of Norway in 1980 by President Julio César Turbay Ayala, post he occupied until 1983 when he was appointed Ambassador to El Salvador where he participated in the crucial peace talks of the Contadora Group.
His diplomatic career reached its highest point as Minister Plenipotentiary to the United States between 1988 and 1990 where he worked closely lobbying the US Congress to advance Colombian interests in passing the Andean Trade Preference Act.
Luis Guillermo Vélez Trujillo died on February 6, 2007, at the Cardio Infantil Clinic in Bogotá after suffering a heart attack.