Duque attended Colegio Rochester and graduated from Sergio Arboleda University in Bogotá in 2000 with a degree in law.[3] He holds an LLM in International Economic Law from American University and a Master's in Public Policy Management from Georgetown University, Washington D.C.. Duque also attended Harvard University, where he studied business and government.[4] He began his professional career in 1999 as a consultant in the Andean Development Corporation (CAF) and later served as an advisor at the Colombian Ministry of Finance and Public Credit during the government of Andrés Pastrana (1998–2002).
Subsequently, he worked at the Inter-American Development Bank (IDB) between 2001 and 2013. There he served as Senior Adviser to the Executive Board for Colombia, Peru and Ecuador, Advisor to the Presidency, and chief of the Division of Culture, Solidarity, and Creativity.
Duque also served a period as international advisor of former President Álvaro Uribe Vélez. Between 2010 and 2011, he was a consultant at the United Nations (UN) in the Research Panel appointed by the Secretary-General for the Incident of the Gaza Flotilla that occurred on May 31st, 2010, between Israel and Turkey, known as Mavi Marmara.