Jovenel Moise, a 48-year-old banana exporter, was sworn in at a ceremony at the National Assembly.
His predecessor, Michel Martelly, stood down a year ago at the end of his term, and was replaced by an interim president while rival political parties disputed the result of the elections.
Haiti is the poorest country in the Americas.
It is still struggling to recover from a series of natural disasters, including a devastating earthquake that hit the capital, Port au Prince, seven years ago.
Mr Moise, who has never before held public office, was appointed by Mr Martelly in 2015 as his preferred candidate.
He won the October 2015 poll, but the election was annulled for alleged fraud.
Mr Martelly left office in February 2016, at the end of his five-year-term, passing on power to Senate President Jocelerme Privert.
A new election was held in November.
It was delayed by a month because of Hurricane Matthew, which destroyed 90% of some of Haiti's southern areas at the beginning of October.
Mr Moise won in the first round, with some 55% of the vote against 20% for his closest rival, Jude Celestin.
But the result is still being contested by the opposition, which held protests outside the National Assembly building.
He is due to lay out his plans for the next five years in a speech later on Tuesday.
Mr Moise and former president Martelly are both members of the centre-right Parti Haitien Tet Kale (Haitian Bald Head Party).
Haiti has sworn in a new president after a political crisis that has lasted more than a year.