Fujimori, 51, received 50.13 per cent of the vote, the South American country's electoral office announced on Monday, more than three weeks after the June 7 run-off.
Her left-wing rival Roberto Sánchez won 49.86 per cent. Just 49,641 votes separated the two candidates.
Fujimori wrote on X that she would await the official announcement of the final results by the national electoral commission in the coming days with "great humility, prudence and responsibility".
"We are getting closer and closer to starting a path of order and hope for all Peruvians," she wrote.
Her opponent had previously said he would not recognise the election results.
Fujimori is the daughter of Peru's late former president Alberto Fujimori, who was convicted of human rights violations.
The politician from the conservative Fuerza Popular party was running for president for the fourth time. She has promised a tough crackdown on organised crime and plans to deregulate the economy.
She will take office on July 28.
The political situation in the country of around 35 million people has long been shaped by constant conflict between Congress and the government.
Congress can remove presidents from office for "moral incapacity." Peru has had eight presidents in the past 10 years.
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