41-yr-old Duque polled just over 54 percent to his leftist rival Gustavo Petro's 41.7 per cent with 97 per cent of the vote counted.
Bogata: Conservative Ivan Duque won Colombia's presidential election on June 18 after a campaign turned into a referendum on a landmark 2016 peace deal with FARC rebels that he pledged to overhaul.
Duque, 41, polled just over 54 percent to his leftist rival Gustavo Petro's 41.7 per cent with 97 per cent of the vote counted, electoral authority figures showed.
Petro, a leftist former mayor and ex-guerrilla, supports the deal. "These are momentous elections," President Juan Manuel Santos, who will step down in August, said as he cast his ballot early in the day. "Let us continue to build a country at peace, a country of democracy, a country which we all hold dear and to which we all contribute."
His efforts to end the war with the Revolutionary Armed Forces of Colombia (FARC) brought him the Nobel Peace Prize, though he is leaving office with record unpopularity in a country of 49 million people.
The world's leading producer of cocaine, the Latin American country continues to battle armed groups vying for control of lucrative narco-trafficking routes in areas FARC once dominated.
Duque's victory means he will be Colombia's youngest president since 1872, during his swearing-in ceremony in August. He comfortably won the first round last month, having campaigned on a pledge to rewrite the agreement signed by Santos.
Duque, 41, says he would revise it in order to sentence guerrilla leaders guilty of serious crimes to "proportional penalties." On Sunday, as he voted surrounded by his children, Duque said he wanted to make sure that those who commit crimes "pay for them."
The former economist and first-term senator says he wants to keep ex-FARC rebels from serving in Congress. The agreement allowed the group to transform itself into a political party.
Duque is buoyed by the backing of his popular mentor, former president and now senator Alvaro Uribe, whose two-term presidency from 2002-2010 was marked by all-out war on the FARC.
Petro, 58, was the first leftist to reach a presidential runoff in Colombia, and believed his presence showed the South American country had shed its suspicions of the left, tainted by 50 years of conflict. "The need to change things is fundamental," he said after voting. "We are going to build a humane Colombia that is at peace, that is reconciled with itself."
A former member of the disbanded M-19 guerrilla group, Petro had promised to implement the agreement with the FARC, whose 7,000 ex-combatants have struggled to return to civilian life.
FARC leader Rodrigo Londono, known as Timochenko during the conflict, said: "With either one of the two (candidates), we cannot let down our guard." Highlighting Colombia's glaring inequalities during his campaign, Petro also said he would buy out land owned by the big agro-industrial companies and redistribute it to poor farmers.
Polls closed at 4:00 pm (2100 GMT) after a day of peaceful voting.