"The people have had their say," he said Thursday in an interview with AFP, adding that it was now time for his rivals "to begin to realize that the country can no longer wallow in this history of violence."
"We need order and discipline to put the country back on the road to development," he said.
Two years ago, the banana farmer and entrepreneur was a little-known political novice. But after former president Michel Martelly chose him to represent his party, Moise, now 48, has become known by the nickname he loves to chant: "the banana man."
With the provisional results giving him a majority of the vote, Moise says he is Haiti's "elected president" -- in defiance of the Provisional Electoral Council (CEP), which had urged political groups, parties and candidates "not to declare themselves elected."
"The council is and remains the only organization qualified to certify the victory of a candidate," the CEP added in a press statement Wednesday.
"The preliminary results indeed said that I am the candidate in first position," said Moise, the candidate of the Tet Kale Party (PHTK).
"That means what? That I am the elected president."
'Barring a miracle...'
"Barring a miracle, and without having to resort to complicated mathematical or statistical computations," Moise said, he would remain in the lead.
But his chief rivals have refused to recognize the results of the November 20 election.
Jude Celestin, who placed second with 19.52 percent of the vote, Moise Jean-Charles (11.04 percent) and Maryse Narcisse (8.99 percent) are all preparing challenges to be presented to the election authorities.
Hundreds of inhabitants from the poorest neighborhoods in the capital -- supporters of Narcisse and her leftist Fanmi Lavalas party -- have been demonstrating since Monday against what they consider an "electoral coup d'etat."
Police on Wednesday forcibly dispersed demonstrators, who broke car windows while fleeing.
Moise said he deplored such violence, adding that it was time for Haitians to turn the page.
"The country can no longer endure this eternal presidential campaign," he said, adding that for his part -- and speaking for his team and members of his party -- "we know we won the election in the first round."
A first round of voting originally took place in October 2015, when Moise also bested his rivals. But the authorities canceled the results of that vote because of widespread complaints and evidence of massive fraud.
'A huge mess'
In February, Haiti's parliament elected Jocelerme Privert, president of the Senate at the time, to be interim president to succeed Martelly, whose five-year term was nearing its end.
Exhausted and disillusioned by an electoral process that began more than a year ago, most Haitians have lost hope that the election will help them out of their extreme poverty: more than 60 percent of the island's inhabitants live on less than $2 a day.
And while Moise may have received 55 percent of the first-round votes, his popularity may be limited: only 21 percent of eligible voters participated in the election.
Moise noted that the lowest participation was in the Ouest (West) department, which includes the capital Port-au-Prince, adding that "as you know, the Ouest is a huge mess."
People there have lost hope and have no faith in politicians, he said.
"I want to build this confidence, to restore it to the people, to Haitian youth," he added.
But Haiti's middle-class youth have turned a deaf ear to the endless electoral promises, increasingly looking to the United States for their salvation.
More than 5,000 Haitians are currently in immigration detention centers in California, while several thousand others have traveled first to Brazil or Chile, where entry visas are easier to obtain.