With 97 per cent of ballots counted till late yesterday, Socialist Party chief Dodon had 55.3 per cent of the votes, according to the electoral commission, with pro-European rival Maia Sandu on 44.7 per cent.
"We have won, everyone knows it," Dodon told a late-night press conference.
Official results were due to be announced at 0800 (local time) today.
The vote marks the first time in 16 years that Moldova -- wracked by corruption scandals in recent years -- is electing its leader by national vote instead of having parliament select the head of state.
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Dodon had come out top in the first round of voting on October 30 with 48 per cent ahead of Sandu, a centre-right former education minister who worked for the World Bank, with 38 per cent.
The two candidates have diametrically opposed visions for Moldova's future.
Dodon -- who served as economy minister under a communist government between 2006 and 2009 -- is calling for deeper ties and boosting trade with Moscow.
Sandu meanwhile urged a path towards Europe, calling for the withdrawal of thousands of Russian troops from the Russian-speaking separatist region of Transdniester, which broke away in the early 1990s after a brief civil war.
The move was bitterly opposed by Russia, which responded with an embargo targeting Moldova's crucial agriculture sector.
"I and all my friends voted for Igor Dodon since he promises to restore the strategic partnership with Russia," said Vasilii Blindu, a 70-year-old pensioner in the northern town of Balti.
But Chisinau student Marcel Pruna, 22, said he backed Sandu because she will "carry out reforms in practice, not just in words".
Both candidates criticised the vote as badly organised, highlighting the shortage of ballot papers for overseas voters. More than 4,000 Moldovan and international observers were on hand to monitor the vote.
The vote comes as a Moscow-friendly general also claimed victory in ex-communist Bulgaria's presidential election Sunday, prompting Prime Minister Boyko Borisov to announce his resignation as his nominee was dealt a crushing defeat.
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