The 52-year-old from the southern island of Tanna becomes the fifth man to lead Vanuatu since 2022, taking over from Charlot Salwai.
Mr Napat, a former deputy prime minister who was a meteorologist before entering parliament, loomed as a likely leader since his Leaders Party's (LPV) strong showing in the January 16 election.
The LPV won nine seats and quickly moved to agree a memorandum of agreement to govern with the Vanua'aku Party, Eagle Group, Reunification Movement for Change (RMC), and Land and Justice Party (GJP).
The five parties control at least 32 MPs in the 52-seat parliament, ensuring control.
On Tuesday, parliament sat for the first time since the election, with Mr Napat elected unopposed after the opposition chose not to test the government's numbers by putting forward a leadership candidate of their own.
In a good sign for the prospect of a harmonious coalition, Mr Napat was nominated for prime minister by Mr Salwai, the RMC leader, and seconded by GPV leader Ralph Regenvanu.
Johnny Koanapo, Vanua'aku Pati leader, is deputy prime minister and finance minister.
Mr Regenvanu, a climate activist who has spearheaded the country's bid for high-emitting countries to do more to arrest global warming, returns as climate change minister.
Mr Salwai was not appointed to a cabinet post.
Stephen Felix, a former Supreme Court Justice from the Leaders Party, was appointed as Speaker.
The five-party rainbow coalition is in keeping with recent practice in Vanuatu, which battles political instability given voters often elect a dozen or more parties to the parliament.
In an address after his appointment, Mr Napat pledged to make essential service delivery his top priority, while committing to political reform to improve stability.
Vanuatu, one of Australia's closest neighbours, is a string of around 80 islands in the Pacific's Melanesian region.
It is also one of the region's poorest nations per capita, reliant on agriculture and tourism.
The capital of Port Vila was rocked by a 7.3 magnitude earthquake in December, which killed at least 14 people and brought great destruction to the city.
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