Center-left Prime Minister Saulius Skvernelis vowed to quit after he was eliminated from the run-off having finished in third place.
Conceding that “the failure to get into the second round is an assessment of me as a politician,” Skvernelis told reporters that he would “step down on July 12.”
He did not rule out early elections. The next regularly-scheduled parliamentary elections are due in October 2020.
Nauseda, promising to seek the political middle-ground and build a welfare state, won 31.07 percent of the vote, according to near-complete official results.
“I want to thank all the people who took to their hearts our message that we want a welfare state in Lithuania and we want more political peace,” Nauseda told reporters in Vilnius.
The 54-year-old is seeking to bridge the growing rich-poor divide in the former Soviet republic of 2.8 million people, which joined the European Union and NATO in 2004.
“Nauseda has a greater chance to attract votes that went to other candidates, especially from the left,” Vilnius University analyst Ramunas Vilpisauskas told AFP.
In all, nine candidates ran in the first round vote.
In second place, Simonyte, who is popular with wealthy, educated urban voters, garnered 29.46 percent of the vote while resonating with the rural poor, Skvernelis’s populist approach secured 20.72 percent support.
Simonyte, 44, a technocrat who also warns against deepening inequality and the rural-urban divide, has vowed to reduce it by boosting growth further.
Socially liberal, Simonyte supports same-sex partnerships which still stir controversy in the predominantly Catholic country.
Simonyte said she would resist “populism” during her second-round campaign and seek support from political forces “with consistent views that do not try to be on the right with one leg and the left with the other.”
Lithuanian presidents steer defense and foreign policy, attending EU and NATO summits, but must consult with the government and the prime minister on appointing the most senior officials.
Popular incumbent President Dalia Grybauskaite, an independent in her second consecutive term, must step down due to term limits.
The politician nicknamed the “Iron Lady” for her strong resolve has been tipped as a contender to be the next president of the European Council.
Both Nauseda and Simonyte are strong supporters of EU and NATO membership as bulwarks against neighboring Russia, especially since Moscow’s 2014 military intervention in Ukraine.
Analyst Vilpisauskas said that both Nauseda and Simonyte are very likely to opt for continuity in foreign and defense policy.
“With Nauseda, there can be some tactical changes when it comes to communication with neighbors but the strategical line is unlikely to change.”
Although Lithuanian presidents do not directly craft economic policy, bread and butter issues and tackling corruption dominated the campaign.
Lithuania is struggling with a sharp decline in population owing to mass emigration to Western Europe by people seeking better opportunities.
The global financial crisis triggered a deep recession 10 years ago and austerity measures imposed to prevent further crisis took a high toll, especially on low-income earners.
Despite solid economic growth, a recent EU report noted that almost 30 percent of Lithuanians “are at risk of poverty or social exclusion” and that this risk is “nearly double” in rural areas.
Robust annual wage growth of around 10 percent has raised the average gross monthly salary to 970 euros ($1,00) but poverty and income inequality remain among the highest in the EU, largely due to weak progressive taxation.
Unemployment stood at 6.5 percent in the first quarter of 2019, and the economy is forecast to grow by 2.7 percent this year, well above an average of 1.1 percent in the 19-member eurozone.
Brussels has urged Vilnius to use solid growth fueled mostly by consumption to broaden its tax base and spend more on social policies.
Nauseda voter Feliksas Markevicius said he wanted the new president to help emigrants to return home to Lithuania.
“We need to improve living conditions because many people are forced to work abroad,” the pensioner told AFP after voting in Vilnius on Sunday.
Voter turnout was 54.96 percent, according to the Central Elections Commission.