Michel replaces Jean Michel Lapin, who earlier announced he was stepping down.
The president made the announcement in a Monday night Twitter post, but must formalise it with an official decree.
Michel's appointment came after consultations between Moise and the leaders of the two chambers of parliament, signaling a resumption of dialogue between the three political heavyweights after months of turmoil.
Moise faces an uphill task in getting his new nominee accepted by legislators who had used various strategies including removing furniture from the Chamber and failing to report for work in a bid to block a vote on Lapin's nomination.
Moise has had his power to appoint ministers challenged and faced calls to resign after the High Court of Auditors in May released a report saying Moise was at the center of an "embezzlement scheme" that siphoned off Venezuelan aid money meant for fixing roads.
"I am looking you right in the eye to tell you today: your president, the one you voted for, is not involved in corruption," Moise responded at an official ceremony in the capital Port-au-Prince last month.
Michel faces the tough task of restoring public confidence in Haiti's leadership.
Sixty percent of Haitians live below the poverty line, the inflation rate has risen past 18 percent and violent crime has surged.
Port-au-Prince is particularly hard-hit, with clashes between armed gangs occurring almost daily.
In a letter addressed to the president, Senate President Carl Murat Cantave confirmed that Jean-Michel Lapin, who served in a caretaker prime minister role since March, had resigned. The resignation, dated July 3, cleared the way for Michel, who is described as a longtime public servant and entrepreneur.
“I don’t think he’s going to make anyone scared,” said Lower Chamber President Gary Bodeau, adding, “I think he’s a better choice than Lapin.”
Bodeau said Michel was not the president’s first choice. And after Cantave objected to Moïse’s preferred candidate, Michel’s name was put on the table by the two lawmakers as a compromise.
The United Nations in June released a report saying that at least 26 people were killed during a 2018 massacre in a slum in the capital, at which several members of the police and a government representative were allegedly present.
Moïse’s first prime minister, Jack Guy Lafontant, a political unknown, was forced to resign in July 2018 after a poorly orchestrated gas hike triggered three days of rioting and the cancellation of international flights.
The second, lawyer Jean Henry Céant, was fired after six months by the Lower Chamber of Deputies. His tenure was marked by anti-government protests and calls for Moïse to step down, as well as nine days of a countrywide lock-down.
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