Environmental lawyer Caputova got 58.4 percent of the ballot while EU energy commissioner Maros Sefcovic garnered 41.5, the Slovak Statistics Office said. Official results are due Sunday at noon.
"Let us look for what connects us. Let us promote cooperation above personal interests," Caputova said after her victory, Press TV reported.
The 45-year-old added that the outcome was a sign that "you can win without attacking your opponents."
"I believe this trend will also be confirmed in the elections to the European Parliament and the Slovak parliamentary elections next year."
Sefcovic, the 52-year-old ruling party candidate, called Caputova to congratulate her and planned to also send flowers.
"The first female president of Slovakia deserves a bouquet," he told reporters.
Prime Minister Peter Pellegrini, who belongs to the governing Smer-SD party, said he expected "constructive cooperation."
Outgoing President Andrej Kiska told reporters that "Slovakia is in a moral crisis and needs a president like Zuzana Caputova."
"Many countries probably envy us for we have chosen a president who symbolizes values like decency."
Political novice Caputova, who ran on a slogan of "Stand up to evil" had earlier called the last few weeks "extremely challenging" and "an intense journey."
No stranger to tough battles, Caputova won a 2016 award for successfully blocking a planned landfill in her hometown of Pezinok.
More recently, she took to the streets of the central European country of 5.4 million along with tens of thousands of other anti-government protesters after investigative journalist Jan Kuciak was gunned down alongside his fiancée in February 2018.
He had been preparing to publish a story on alleged ties between Slovak politicians and the Italian mafia.
The killings forced then Prime Minister Robert Fico to resign but he remains leader of the populist-left Smer-SD and is a close ally of the current premier.
Five people have been charged, including a millionaire businessman with alleged Smer-SD ties who is suspected of ordering the murders.
The European Parliament has urged Slovakia to look into "any possible political links to the crimes."
MEPs voiced "concern about the allegations of corruption, conflicts of interest, impunity and revolving doors in Slovakia's circles of power."
Speaking to AFP on the campaign trail, Caputova said she would "initiate systematic changes that would deprive prosecutors and the police of political influence."
In addition to fighting for justice for all, Caputova has promised better care for the elderly and environmental protection.
Observers have compared Caputova to French President Emmanuel Macron, an outsider who swept to power on a reformist agenda.
Though the office is largely ceremonial, the president ratifies international treaties, appoints top judges, is commander-in-chief of the armed forces and can veto laws passed by parliament.