Appointed by decree, Jean will work on forming a government before delivering a policy statement to Haitian lawmakers.
Privert took office on February 14, a week after the departure of president Michel Martelly, who left without a successor after a vote to choose his replacement was postponed over fears of violence.
Under an agreement signed hours before Martelly's departure, the interim president, who was chosen by parliament, will serve for up to 120 days.
Haiti is the poorest country in the Americas, still struggling to get back on its feet after being hobbled by devastating 2010 and now plunged into a drawn-out electoral crisis.
There is still much uncertainty over the country's ability to hold presidential and legislative elections within the next four months.