With 99.9 per cent of ballots counted, Socialist Party chief Dodon had 52.3 per cent of the votes, according to the electoral commission, with pro-European rival Maia Sandu on 47.7 per cent.
"We have won, everyone knows it," Dodon told a press conference overnight.
The full results are expected to be announced later this week.
Kremlin spokesman Dmitry Peskov said Moscow respected the results of the Moldovan vote and congratulated its winner.
The vote marks the first time in 20 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.
They have diametrically opposed visions for Moldova's future.
Dodon -- who served as economy minister under a communist government between 2006 and 2009 -- has called for deeper ties and boosting trade with Moscow.
Sandu meanwhile had 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.
"Close ties united us with Moldova before but then the scope of our relations slid," Peskov told journalists Monday.
"But Russia has always been and remains committed to maintaining ties with Moldova."
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.
Turnout was 53.4 percent, the electoral commission said.
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