Sandu, also leader of the Party of Action and Solidarity, was leading with 57 percent, while incumbent President Igor Dodon, another contender for Moldova's highest position in the next four years, was lagging behind with 43 percent, said the country's Central Electoral Commission.
For her part, Sandu, who was defeated by Dodon in the 2016 presidential elections, said that her first step as a new head of State will be to achieve 'the unity of society around one goal'.
"Moldova has a future thanks to the good people in this country", she said.
Moldova is also one of Europe's poorest countries, with 40 percent of its citizens moving overseas for work.
"I urge everyone to calm, regardless of the election results". Incumbent President Igor Dodon was supported by over 40% of voters.
In the first round vote earlier this month, she won a surprise victory against Dodon.
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Celebrations broke out overnight in front of opposition headquarters in the centre of the capital Chisinau, with supporters chanting: "President Maia Sandu" and "a country for young people".
At a rally in Chisinau, Dodon called on his supporters to protest against the results. Few would admit to that publicly, but by preferring to utter polite but ultimately meaningless statements about a "strong partnership" and "support for Moldova's European integration", as opposed to explicit support for unification, they do just that.
Moldova has close historical ties with neighbouring Romania and they share a common language.
"I say to those who voted for my opponent - you did not lose, I will earn your trust every day". It relies heavily on remittances, and closer ties with the European Union are generally seen as more likely than those with Moscow to lead to a long-elusive political stability and economic recovery.
Russian Federation stations troops in Moldova's Moscow-backed region of Transnistria, which broke away after a brief civil war following the collapse of the USSR in 1991 and is not internationally recognised.
If Sandu wins, she is likely to seek a snap parliamentary election to consolidate power because parliament is controlled by the Socialists, Dodon's former party.