According to the electoral commission, economist Pedo Pablo Kuczynski received 50.12% of votes, against 49.88% for his rival, Keiko Fujimori.
About 50,000 ballots must first be settled by an electoral court before a winner can be officially declared.
Keiko Fujimori has yet to concede, but Pedro Pablo Kuczynski tweeted his thanks to the Peruvian people: “It’s time to work together for the future of our country.”
This has been the tightest fought election in Peru in five decades.
As the last few votes were counted, the candidates remained neck-and-neck, with Pedro Pablo Kuczynski leading by a tiny margin.
The closeness of the result came as a surprise after polls in the run-up to the election had suggested Keiko Fujimori had a comfortable lead.
Analysts said corruption scandals in Keiko Fujimori’s Popular Force Party may have dented her support since April, when she comfortably won the first round of voting.
Keiko Fujimori is the daughter of Peru’s former President Alberto Fujimori, who is in jail for crimes against humanity.
Pedro Pablo Kuczynski, who is an ex-Wall Street financier, said he would use his international financial experience to promote economic growth.
He has the support of prominent figures such as Nobel-Prize-winning novelist Mario Vargas Llosa and left-wing candidate Veronika Mendoza, who came third in the first round of voting.
However, Pedro Pablo Kuczynski he has faced scrutiny over his close relationship to Peru’s business elite.
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