The party won 25% of the vote and 53 seats in the 150-seat parliament in a move that steered the country to the right, according to results released by the Statistics Office.
Slovakia has been dominated by the social democratic left-wing populists SMER-SD, led by former Prime Minister Robert Fico, since 2006. In the 2016 election, the leftist party gained 28.3% of votes after campaigning on an anti-migrant ticket.
This time, the SMER-SD party came in second with 18.3% of the vote, winning about 38 seats.
Since the February 2018 murder of journalist Jan Kuciak — who had been investigating the misuse of EU funds in Slovakia, tax fraud and alleged ties between government officials and the Italian mafia — the party’s popularity tumbled.
"After Ján Kuciak's murder, a massive breakthrough occurred in a part of society. The people's cup of patience had flowed over," Slovak political analyst Marián Sekerák told Euronews.
"This murder could be recorded in Slovak history as a turning point ... it helped to fully [expose] the interconnection of clientelistic and mafia structures with the highest political figures."
Centre-right Ordinary People (OLANO) chairman Igor Matovič told Euronews that he wants to create "the best government in the history of Slovakia".
"The best one, with no corruption. I hope that it will be a government for all the people in Slovakia not just for the rich ones," he said.
Pro-western Matovič, 46, has made fighting corruption and attacking Fico the central tenet of his campaign. His party has been running on an anti-corruption platform.
Matovič is most likely to become prime minister and is expected to govern with the pro-business Freedom and Solidarity party that won 6.2% (13 seats) and the conservative For People established by former President Andrej Kiska that finished with 5.8% (12 seats).
Although the three would have a majority with 78 seats, Matovič said he also wants to rule with French politician Marine Le Pen's ally, We Are Family, a populist right group that placed third with 8.2% or 17 seats.
"I'd like to assure everybody that there's nothing to worry about,'' he said. "We're not here to fight cultural wars."
It's hard to estimate whether their partnership can survive the whole four-year term.
Far-right gains seats in Slovakia
Meanwhile, in what is likely to be a further blow to SMER, the party's two current coalition partners, the ultra-nationalist Slovak National Party and a party of ethnic Hungarians, looked like they wouldn't win any seats.
An extreme far-right party whose members use Nazi salutes and which wants Slovakia out of the European Union and NATO became the fourth most popular party in the country of just under 5.5 million with 8% and 17 seats.
The far-right People's Party Our Slovakia had won 8% and 14 seats in parliament in 2016.
All other parties have ruled out cooperation with the party that advocates for the legacy of the Slovak Nazi puppet World War II state.
Which parties will form the new government?
Despite the victory of OLANO, the populist group will need to secure the support of other parties to form a government.
According to Dr Philipp Köker, who is a research fellow at the Leibniz University Hannover, OLANO’s most natural coalition partners are the libertarian Freedom and Solidarity and the centrist For the People led by former president Andrej Kiska. Together, these parties would have a slim majority of three seats in the National Council.
Another potential coalition partner could be the conservative and nationalist We Are Family, founded by the businessman and tabloid personality Boris Kollár.
The ousted SMER or the neo-Nazi party People's Party are not likely to be part of the equation.
"If these four parties reach an agreement they would have the qualified majority in Parliament needed to amend the Constitution," Slovak political analyst Marián Sekerák said.
Some fundamental changes to the judiciary and prosecution can only be made by direct intervention in the Constitution. "These parties have declared their readiness to make such changes", Sekerák said.
What is the agenda of the Ordinary People party?
The party relies upon the success of its leader, the millionaire Matovič.
OLANO's main aim is to create new anti-corruption measures, including enhanced public transparency and reform of the judiciary and public procurement.
The party also wants to improve health care by replacing old hospitals and bringing them up to EU standards, Dr Köker said.
It aims to reform the new contributions to the social insurance system and address regional disparities in the economy by using funds from the EU more effectively.
However, Radoslav Štefančík, a political analyst from the University of Economics in Bratislava told Euronews that the Ordinary people "will not support the liberalization of society", and that it will have a reserved approach to the rights of homosexuals.
"OLANO does not want to lift the populist measures taken in parliament by the former government coalition," Štefančík said.
