The Deputy Prime Minister will be joined by Conservative Investment Minister Lord Livingston and Mexico Trade Envoy Liberal Democrat peer Baroness Bonham-Carter, as well as more than 40 UK business leaders, seeking to tap into the two countries' investment potential.
Mr Clegg said Britain's presence in Colombia and Mexico had been "too small, too reticent and too modest for far too long".
Speaking ahead of his visit, he said: "The UK took its eye off the Latin American ball, and as a result we've fallen behind many of our other European competitors."
Mr Clegg will meet Mexico's reforming President, Enrique Pena Nieto, for the second time to reiterate the UK's commitment to strengthening its bilateral trade relations, building on his previous visit in March 2011 and Mr Pena Nieto's visit to the UK in June 2013. Mr Clegg is set to announce a new target to double the UK's market share in Mexico to 1.5% by 2020.
He will also be the most senior British Government Minister to visit Colombia since 1992. He and President Juan Manuel Santos are set to discuss the terms of a new trade and investment target for Colombia, worth £4 billion by 2020.
HSBC bank, jet engine manufacturers Rolls-Royce, commercial banknote printer De La Rue, oil and energy firm Shell, and designer architects Zaha Hadid are among business names also on the trip.