Provisional Electoral Council chief Uder Antoine said Moise came ahead of Jude Celestin, candidate of the opposition LAPEH, scoring 55.67 per cent against 19.52 per cent.
Moise Jean Charles got 11.04 per cent and Maryse Narcisse 8.99 per cent.
Any candidate who wins more than half of the votes cast is considered the victor.
Haitian law offers candidates the opportunity to challenge the results from the presidential and legislative election in electoral courts, before final results are due to be published on December 29.
Interim leader Jocelerme Privert called for calm ahead of the vote result announcement.
"Resorting to acts of violence can only spoil the fruits of the beautiful day we had on November 20," Privert said at the presidential palace in Port-au-Prince, referring to the vote held earlier this month.
The election was a key step in restoring constitutional order in Haiti, where Martelly's mandate expired after the results of last year's first round poll were annulled amid widespread claims of fraud.
Of the 27 candidates who ran for president, four had claimed victory in the first round before the official announcement in statements criticized by the international community.
"My compatriots, our country is living through a dramatic moment. It needs a social cooling off, it needs calm, serenity, peace and tranquility," Privert said.
"My brothers and sisters, I invite you all to use the means of recourse set forth in the electoral decree and constitutional provisions to defend your legitimate rights."
With the results annulled, Martelly, a popular singer elected in May 2011, was unable to transfer power to a successor chosen by popular vote, as required by the constitution.
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