De La Espriella had 49.65 per cent of the vote while his rival, Senator Ivan Cepeda, trailed by some 246,000 votes at 48.70 per cent, according to an initial tally of the runoff election from the country's national registrar on Sunday.
Cepeda, 63, had vowed to continue the policies of President Gustavo Petro, a former rebel and the country's first leftist president, including state pension payments for the poor, union-backed labour reforms, a moratorium on new oil projects, and peace talks with armed groups that have fought the state for decades.
De La Espriella has blamed Petro for the country's economic and security troubles and has vowed to end talks with rebels and criminal groups, while boosting the oil and gas sector, lowering taxes and reducing the size of the state by up to 40 per cent.
He has said, however, that he will preserve Petro's 23 per cent increase in the minimum wage, along with other popular social measures.
"It is a victory for Colombia - a change after four lost years with no clear direction," said Viviana Olivos, a 46-year-old mechanical engineer, as she gathered with other De La Espriella supporters in coastal Barranquilla to hear him speak at a scheduled appearance later on Sunday.
The closeness of the race, with less than one percentage point separating the two candidates, will likely force De La Espriella to water down some of his proposals in order to get support from a divided Congress.
Cepeda's Historic Pact party has more seats than any other party in both the Senate and the lower house, although no party has a majority.
De La Espriella, a lawyer with no prior political experience, will also have to grapple with high public debt.
In a short live-stream appearance on his YouTube channel, he said he had spoken with US President Donald Trump, who offered his congratulations.
Major business guilds, including the Colombo-American Chamber of Commerce, the mining association and the banking association, published statements congratulating De La Espriella on his victory.
In upper- and middle-class neighbourhoods in Bogota and Medellin, flag-waving supporters cheered, honked car horns and set off fireworks.
More than 26.3 million Colombians cast ballots of the 41.4 million eligible to vote.
Some 426,000 voters turned in blank ballots, usually seen as a protest vote, the registrar figures showed.
Cepeda told his supporters at an event in Bogota that he would await a final, ballot-by-ballot check of the initial count, saying his campaign is challenging results from some 33,000 ballot boxes, out of 122,000 in total.
His supporters are a significant political force, he added, and must have a seat at the table.
"We are open to dialogue; we are willing to reach agreements as long as they are respectful, genuine, and reflected in political actions that benefit the nation and preserve the historical progress we have already achieved," Cepeda said.
