Marape returns to the top job after turbulent general elections marred by claims of election fraud, widespread violence, deaths, and major damage to infrastructure across the country.
Marape, whose Pangu Party has won at least 36 of 118 seats, is set to lead a coalition government made up of at least 17 different parties.
So far 105 seats have been confirmed and votes continued to be counted for 13 seats.
For the first time in several years, women candidates have been elected to the Papua New Guinea parliament.
Rufina Peter, 52, an economist and member of the main opposition party People's National Congress, was one of two women elected.
She won the Central Province electorate where she will also serve as governor.
Last month PNG police and electoral authorities were on the verge of declaring failed elections in some of the country, as a school and other buildings were set alight in Enga Province and attempts were made in Hela Province to remove ballot boxes.