He began his journalistic career in the Citynoticias newscast on Citytv (Colombia), the television channel of the newspaper El Tiempo. Subsequently, he worked for Enron as a financial analyst in Houston, Texas. In 2003 he resumed his journalistic career, and joined Caracol Noticias as international editor and head of international correspondents.
In 2004, he was appointed director and presenter of Portafolio TV, the first Colombian business and economy program on Citytv. At the same time, he directed and presented the Citynoticias information system, Bogotá en Punto.
Since December 2005 he was host and producer of CNN International. He was in charge of the programs and sections on the chain's economy and business.
In January 2006, Velez joined CNN as host and producer for CNN en Español. He was director of CNNE's Economics Unit, presenter of Executive Agenda, and was part of CNN's special coverage division where he covered events such as the earthquake in Haiti, the 2008 United States presidential elections, the crisis of 30 of September in Ecuador and President Mahmood Ahmadinejad's tour of Latin America. Subsequently, he was a presenter for CNN International's World Business Today.
On March 2, 2012, he was appointed news director of Caracol Televisión on March 9, 2012. Working with the Noticias Caracol journalistic group, he made special coverage of different news events around the world. He also directed and presented the space called 7/24, on Wednesdays, and was the central presenter of the latest edition of the newscast, from Monday to Friday at 11:30 p.m.
On December 19, 2014, he resigned from the position of director of Noticias Caracol. Caracol Televisión described Vélez's contribution to the channel as invaluable.
On January 28, 2015, he was appointed as the new executive vice president of news for the Telemundo network in Miami, United States, after an investment by his family in said network.
Vélez was a member of the board of the program 6 AM Hoy por Hoy of Caracol Radio. He is currently a columnist for the newspaper El Espectador, news director of La FM owned by RCN Radio and main interviewer for Semana Magazine. It won an Emmy Award for Best Breaking News Coverage in 2015.